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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.3-e
• Conductor: 96.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 96.3-e over \(\Q(\sqrt{57}) \)

Isogeny class 96.3-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
96.3-e1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 1983 a - 8454\) , \( -92476 a + 395358\bigr] \)
96.3-e2	\( \bigl[a\) , \( 0\) , \( a\) , \( 14 a - 62\) , \( 211 a - 903\bigr] \)
96.3-e3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( a - 3\) , \( -3 a - 13\bigr] \)
96.3-e4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -19 a - 83\) , \( -203 a - 693\bigr] \)
96.3-e5	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6645 a - 21759\) , \( 573817 a + 1879205\bigr] \)
96.3-e6	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -106275 a - 348039\) , \( 36664885 a + 120074465\bigr] \)