# ed25519 base point coordinates

For the ed25519 standard Base Point is $$B = (x, 4/5)$$. According to Stack Question the y coordinate equals

46316835694926478169428394003475163141307993866256225615783033603165251855960


But how this value is received? As I understand $$y = 4 \cdot 5^{-1} \mod l$$, where $$l = 2^{252} + 27742317777372353535851937790883648493$$.

So $$5^{-1} \mod l$$ gives

1447401115466452442794637312608598848171423271875981521200390187657090850198


and then $$4 \cdot 5^{-1} \mod l$$ calculates to

5789604461865809771178549250434395392685693087503926084801560750628363400792


Where do I make the mistake?

• It's 4/5 mod p (the prime), not mod l (the group order). Jul 21, 2021 at 14:13
• What is the value of p? Jul 21, 2021 at 14:13
• 2^255 - 19, according to Google (which probably explains the curve name). Jul 21, 2021 at 14:14
• Yes, that's the origin of the name. Similarly, Poly1305 has nothing to do with the value 1305 :) Jul 21, 2021 at 14:15
• Oh, yes. I am foolish. Thank you very much! Jul 21, 2021 at 14:16