I have similar 1440x2560 display, it did not work out-of-the-box with Jetson Nano but I managed to get it to work. This is known bug in Nvidia HDMI driver, it has issues with 2.5K and 4K displays which have native portrait orientation. It is still not fixed in latest L4T release. Hopefully they fix it in next release. See this forum thread for more information: 1440x2560 HDMI display not working - #7 by Lissanro.
This how I managed to get my 2.5K display to work with Jetson Nano: to add support for 2.5K and 4K displays with portrait orientation, I downloaded L4T source code (https://developer.nvidia.com/embedded/linux-tegra), applied the patch below, compiled the kernel and installed it.
diff --git a/kernel/nvidia/drivers/video/tegra/dc/hdmi2.0.c b/kernel/nvidia/drivers/video/tegra/dc/hdmi2.0.c
index c8e34a298..88af19715 100644
--- a/kernel/nvidia/drivers/video/tegra/dc/hdmi2.0.c
+++ b/kernel/nvidia/drivers/video/tegra/dc/hdmi2.0.c
@@ -321,7 +321,7 @@ static bool tegra_hdmi_fb_mode_filter(const struct tegra_dc *dc,
if (!mode->pixclock)
return false;
- if (mode->xres > 4096 || mode->yres > 2160)
+ if ((mode->xres > 4096 || mode->yres > 2160) && (mode->xres > 2160 || mode->yres > 4096))
return false;
#if defined(CONFIG_TEGRA_YUV_BYPASS_MODE_FILTER)
If you do not know how to compile the kernel, please let me know and I will explain how to do it step-by-step. It is relatively easy once you know how to do it.
I also have deb packages with fixed kernel, I build them on Jetson Nano 4GB B01 with JetPack 4.5. In theory my deb files may work for other Jetson Nano models but I tested them only on B01. If somebody interested in pre-built kernel with support for 2.5K and 4K displays, I can share my kernel deb packages but they only work with JetPack 4.5.