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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-5324.7-c
• Conductor: 5324.7
• Rank: \( 1 \)

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

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

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

Isogeny class 5324.7-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
5324.7-c1	\( \bigl[1\) , \( 1\) , \( a\) , \( 157 a + 140\) , \( 3795 a - 654\bigr] \)
5324.7-c2	\( \bigl[1\) , \( a\) , \( 1\) , \( 48 a - 320\) , \( 3251 a + 758\bigr] \)
5324.7-c3	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 537 a + 109\) , \( 192 a + 7744\bigr] \)
5324.7-c4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 307 a - 849\) , \( 4407 a - 7821\bigr] \)
5324.7-c5	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 8297 a + 1789\) , \( 17536 a + 527872\bigr] \)
5324.7-c6	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 4707 a - 13169\) , \( 291111 a - 525613\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph