Elliptic curve isogeny class 256.1-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-256.1-e
• Conductor: 256.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 256.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 256.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
256.1-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a + 76\) , \( 0\bigr] \)
256.1-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 19\) , \( 0\bigr] \)
256.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 66 a - 209\) , \( 518 a - 1638\bigr] \)
256.1-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 66 a - 209\) , \( -518 a + 1638\bigr] \)