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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.4-d
• 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

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

Isogeny graph

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

Isogeny class 96.4-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
96.4-d1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 749 a - 3204\) , \( -17453 a + 74611\bigr] \)
96.4-d2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 11334 a - 48454\) , \( -1274937 a + 5450251\bigr] \)