Elliptic curve isogeny class 9.1-c over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-9.1-c
• Conductor: 9.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{97}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 24 \); class number \(1\).

Elliptic curves in class 9.1-c over \(\Q(\sqrt{97}) \)

Isogeny class 9.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9.1-c1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 46 a - 249\) , \( 396 a - 2148\bigr] \)
9.1-c2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 120608 a - 654229\) , \( -50544244 a + 274173658\bigr] \)
9.1-c3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 7668 a - 41594\) , \( -758664 a + 4115319\bigr] \)
9.1-c4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -7668 a - 33926\) , \( 758664 a + 3356655\bigr] \)
9.1-c5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -46 a - 203\) , \( -396 a - 1752\bigr] \)
9.1-c6	\( \bigl[1\) , \( 1\) , \( 0\) , \( -120608 a - 533621\) , \( 50544244 a + 223629414\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph