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

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

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

Isogeny graph

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

Isogeny class 96.5-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
96.5-h1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -14 a - 45\) , \( -14 a - 46\bigr] \)
96.5-h2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -214 a - 700\) , \( 2805 a + 9186\bigr] \)