Elliptic curve isogeny class 96.4-l over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.4-l
• Conductor: 96.4
• Rank: \( 0 \)

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

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

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

Elliptic curves in class 96.4-l over \(\Q(\sqrt{57}) \)

Isogeny class 96.4-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
96.4-l1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 6007 a - 25637\) , \( -495669 a + 2118999\bigr] \)
96.4-l2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2727736 a - 11660855\) , \( 3260456517 a - 13938181707\bigr] \)
96.4-l3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 1060616 a - 4534055\) , \( -1114243483 a + 4763298645\bigr] \)
96.4-l4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -32262 a - 105654\) , \( 6009228 a + 19679724\bigr] \)