Elliptic curve isogeny class 5324.6-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-5324.6-b
• Conductor: 5324.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 5324.6-b over \(\Q(\sqrt{-7}) \)

Isogeny class 5324.6-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5324.6-b1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 16 a - 2\) , \( 0\bigr] \)
5324.6-b2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -64 a + 8\) , \( -136 a + 138\bigr] \)
5324.6-b3	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -16 a + 62\) , \( 130 a + 30\bigr] \)
5324.6-b4	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9 a - 62\) , \( 51 a - 162\bigr] \)

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