Elliptic curve isogeny class 6.1-a over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-6.1-a
• Conductor: 6.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 6.1-a over \(\Q(\sqrt{97}) \)

Isogeny class 6.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
6.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 9\) , \( -2 a - 8\bigr] \)
6.1-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -2712803 a - 12002595\) , \( 3673224085 a + 16251918802\bigr] \)
6.1-a3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 4 a - 16\) , \( -a - 10\bigr] \)
6.1-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -39418998 a - 174406545\) , \( 298973036324 a + 1322784942502\bigr] \)

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