Elliptic curve isogeny class 23716.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-23716.5-e
• Conductor: 23716.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 23716.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 23716.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
23716.5-e1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -129 a - 26\) , \( -294 a + 2776\bigr] \)
23716.5-e2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 128 a - 155\) , \( 293 a + 2482\bigr] \)
23716.5-e3	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -268 a - 236\) , \( 3000 a + 28\bigr] \)
23716.5-e4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 269 a - 504\) , \( -2732 a + 2524\bigr] \)
23716.5-e5	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4188 a - 3596\) , \( 192280 a + 13020\bigr] \)
23716.5-e6	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4189 a - 7784\) , \( -188092 a + 197516\bigr] \)

Rank

Rank: \( 0 \)

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