Elliptic curve isogeny class 96.5-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.5-c
• Conductor: 96.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Rank

Rank: \( 1 \)

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

Elliptic curves in class 96.5-c over \(\Q(\sqrt{57}) \)

Isogeny class 96.5-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
96.5-c1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2173 a - 7114\) , \( -491496 a - 1609608\bigr] \)
96.5-c2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -927 a + 3963\) , \( -62397 a + 266742\bigr] \)
96.5-c3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 528 a - 2257\) , \( -10134 a + 43322\bigr] \)
96.5-c4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2328 a - 9952\) , \( 112041 a - 478966\bigr] \)