Elliptic curve isogeny class 5324.7-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-5324.7-e
• Conductor: 5324.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 5324.7-e over \(\Q(\sqrt{-7}) \)

Isogeny class 5324.7-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5324.7-e1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -14 a + 12\) , \( 15 a - 13\bigr] \)
5324.7-e2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 66 a - 58\) , \( 71 a + 59\bigr] \)
5324.7-e3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7 a - 54\) , \( -59 a - 165\bigr] \)
5324.7-e4	\( \bigl[1\) , \( -a\) , \( 0\) , \( 16 a + 46\) , \( -130 a + 160\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph