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

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

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

Curve label	Weierstrass Coefficients
23716.5-j1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -333 a - 197\) , \( 3963 a - 893\bigr] \)
23716.5-j2	\( \bigl[1\) , \( a\) , \( 0\) , \( 116 a + 192\) , \( -1130 a + 3324\bigr] \)
23716.5-j3	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 269 a - 130\) , \( -1047 a - 2267\bigr] \)
23716.5-j4	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -5443 a - 3137\) , \( 250517 a - 46169\bigr] \)

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