Elliptic curve isogeny class 256.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-256.4-a
• Conductor: 256.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 256.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
256.4-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 10\) , \( 8 a - 20\bigr] \)
256.4-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 5\) , \( -11 a + 5\bigr] \)
256.4-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \)
256.4-a4	\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph