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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-256.1-e
• Conductor: 256.1
• Rank: \( 2 \)

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

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

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

Isogeny class 256.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.1-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 10\) , \( 6 a + 16\bigr] \)
256.1-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 10\) , \( -6 a + 16\bigr] \)
256.1-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 64 a - 170\) , \( -434 a + 1148\bigr] \)
256.1-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -64 a - 170\) , \( 434 a + 1148\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph