Elliptic curve isogeny class 8100.2-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-8100.2-b
• Conductor: 8100.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 8100.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 8100.2-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
8100.2-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \)
8100.2-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 13\) , \( -61\bigr] \)
8100.2-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \)
8100.2-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -617\) , \( 5231\bigr] \)
8100.2-b5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -167\) , \( -709\bigr] \)
8100.2-b6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \)
8100.2-b7	\( \bigl[1\) , \( -1\) , \( 1\) , \( -2597\) , \( -50281\bigr] \)
8100.2-b8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -48002\) , \( 4059929\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph