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

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

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

Curve label	Weierstrass Coefficients
96.4-h1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -347 a + 1474\) , \( 2233 a - 9551\bigr] \)
96.4-h2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 22 a + 71\) , \( 41 a + 113\bigr] \)
96.4-h3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -8 a - 19\) , \( -7 a - 19\bigr] \)
96.4-h4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 45\) , \( 71 a - 303\bigr] \)
96.4-h5	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11681 a - 38253\) , \( 1289371 a + 4222583\bigr] \)
96.4-h6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -186861 a - 611953\) , \( 84731071 a + 277487243\bigr] \)