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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-23716.5-g
• Conductor: 23716.5
• Rank: \( 1 \)

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

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

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

Isogeny class 23716.5-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
23716.5-g1	\( \bigl[1\) , \( 1\) , \( a\) , \( 332 a - 529\) , \( -3964 a + 3071\bigr] \)
23716.5-g2	\( \bigl[1\) , \( a\) , \( 1\) , \( -269 a + 139\) , \( 1047 a - 3314\bigr] \)
23716.5-g3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -116 a + 308\) , \( 1130 a + 2194\bigr] \)
23716.5-g4	\( \bigl[1\) , \( 1\) , \( a\) , \( 5442 a - 8579\) , \( -250518 a + 204349\bigr] \)

Rank

Rank: \( 1 \)

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