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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.4-b
• Conductor: 96.4
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
96.4-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 17 a - 82\) , \( -51 a + 213\bigr] \)
96.4-b2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 9508 a - 40648\) , \( 727273 a - 3109031\bigr] \)
96.4-b3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -23702 a + 101322\) , \( 4672577 a - 19974879\bigr] \)
96.4-b4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -581 a - 1895\) , \( 14004 a + 45867\bigr] \)