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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-5324.6-e
• 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-e over \(\Q(\sqrt{-7}) \)

Isogeny class 5324.6-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
5324.6-e1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -40 a + 50\) , \( 45 a - 83\bigr] \)
5324.6-e2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -22 a - 43\) , \( 58 a - 9\bigr] \)
5324.6-e3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -132 a - 483\) , \( -1724 a - 3749\bigr] \)
5324.6-e4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -330 a + 540\) , \( 1213 a + 4369\bigr] \)
5324.6-e5	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -76 a - 127\) , \( -548 a - 387\bigr] \)
5324.6-e6	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -130 a + 152\) , \( -27 a + 1015\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph