Elliptic curve isogeny class 4356.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.5-e
• Conductor: 4356.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 4356.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.5-e contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
4356.5-e1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
4356.5-e2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
4356.5-e3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
4356.5-e4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph