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

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

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

Isogeny graph

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

Isogeny class 96.4-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
96.4-e1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -16 a - 48\) , \( -212 a - 692\bigr] \)
96.4-e2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 106276 a - 454300\) , \( -36558610 a + 156285050\bigr] \)
96.4-e3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 6646 a - 28390\) , \( -567172 a + 2424632\bigr] \)
96.4-e4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -1975 a - 6465\) , \( 86004 a + 281655\bigr] \)
96.4-e5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 7 a + 4\) , \( 36\bigr] \)
96.4-e6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 27 a - 96\) , \( 100 a - 464\bigr] \)