Elliptic curve isogeny class 42588.2-l over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-42588.2-l
• Conductor: 42588.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 42588.2-l over \(\Q(\sqrt{-7}) \)

Isogeny class 42588.2-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
42588.2-l1	\( \bigl[1\) , \( 0\) , \( 0\) , \( 43\) , \( 255\bigr] \)
42588.2-l2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -27\) , \( 45\bigr] \)
42588.2-l3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -7\) , \( -7\bigr] \)
42588.2-l4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -417\) , \( 3243\bigr] \)

Rank

Rank: \( 0 \)

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