Elliptic curve isogeny class 20412.2-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-20412.2-d
• Conductor: 20412.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 20412.2-d over \(\Q(\sqrt{-7}) \)

Isogeny class 20412.2-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
20412.2-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1062\) , \( 13590\bigr] \)
20412.2-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -12\) , \( 24\bigr] \)
20412.2-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 93\) , \( -235\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph