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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-256.1-g
• Conductor: 256.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
256.1-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
256.1-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a - 127\) , \( 0\bigr] \)
256.1-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 528 a - 1397\) , \( 10710 a - 28336\bigr] \)
256.1-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 528 a - 1397\) , \( -10710 a + 28336\bigr] \)

Rank

Rank: \( 1 \)

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