Elliptic curve isogeny class 96.3-g over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.3-g
• Conductor: 96.3
• 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 96.3-g over \(\Q(\sqrt{57}) \)

Isogeny class 96.3-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
96.3-g1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 6\) , \( 2 a + 22\bigr] \)
96.3-g2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 19 a - 59\) , \( -57 a + 271\bigr] \)