Elliptic curve isogeny class 25088.4-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-25088.4-e
• Conductor: 25088.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 25088.4-e over \(\Q(\sqrt{-7}) \)

Isogeny class 25088.4-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
25088.4-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3283 a + 593\) , \( -77889 a + 87207\bigr] \)
25088.4-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 378 a + 355\) , \( 2695 a - 8107\bigr] \)
25088.4-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -203 a + 33\) , \( -1169 a + 1415\bigr] \)
25088.4-e4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -34 a + 667\) , \( 5199 a - 5411\bigr] \)
25088.4-e5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 78 a - 5\) , \( -243 a - 805\bigr] \)
25088.4-e6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 106 a - 173\) , \( 747 a - 203\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph