Elliptic curve isogeny class 256.1-j over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-256.1-j
• Conductor: 256.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 256.1-j over \(\Q(\sqrt{7}) \)

Isogeny class 256.1-j contains 8 curves linked by isogenies of degrees dividing 28.

Curve label	Weierstrass Coefficients
256.1-j1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( -2 a\bigr] \)
256.1-j2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( 2 a\bigr] \)
256.1-j3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 240 a - 725\) , \( 3698 a - 9520\bigr] \)
256.1-j4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 240 a - 725\) , \( -3698 a + 9520\bigr] \)
256.1-j5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -85\) , \( -114 a\bigr] \)
256.1-j6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -85\) , \( 114 a\bigr] \)
256.1-j7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -240 a - 725\) , \( -3698 a - 9520\bigr] \)
256.1-j8	\( \bigl[0\) , \( 0\) , \( 0\) , \( -240 a - 725\) , \( 3698 a + 9520\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 7 & 28 & 4 & 2 & 14 & 4 & 28 \\ 7 & 1 & 4 & 28 & 14 & 2 & 28 & 4 \\ 28 & 4 & 1 & 28 & 14 & 2 & 7 & 4 \\ 4 & 28 & 28 & 1 & 2 & 14 & 4 & 7 \\ 2 & 14 & 14 & 2 & 1 & 7 & 2 & 14 \\ 14 & 2 & 2 & 14 & 7 & 1 & 14 & 2 \\ 4 & 28 & 7 & 4 & 2 & 14 & 1 & 28 \\ 28 & 4 & 4 & 7 & 14 & 2 & 28 & 1 \end{array}\right)\)

Isogeny graph