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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-23716.5-o
• 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-o over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
23716.5-o1	\( \bigl[1\) , \( a\) , \( a\) , \( 28 a - 18\) , \( -47 a - 46\bigr] \)
23716.5-o2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 13\) , \( 13\bigr] \)
23716.5-o3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -57\) , \( 41\bigr] \)
23716.5-o4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -29 a + 10\) , \( 46 a - 93\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph