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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.5-e
• 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-e over \(\Q(\sqrt{57}) \)

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

Curve label	Weierstrass Coefficients
96.5-e1	\( \bigl[a\) , \( -a\) , \( 0\) , \( 14 a - 60\) , \( 95 a - 406\bigr] \)
96.5-e2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -173 a - 571\) , \( -466 a - 1529\bigr] \)
96.5-e3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -118 a - 391\) , \( 1076 a + 3521\bigr] \)
96.5-e4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -1918 a - 6286\) , \( 83966 a + 274979\bigr] \)