Elliptic curve isogeny class 23716.6-h over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-23716.6-h
• Conductor: 23716.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 23716.6-h over \(\Q(\sqrt{-7}) \)

Isogeny class 23716.6-h contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
23716.6-h1	\( \bigl[1\) , \( 0\) , \( a\) , \( 11 a - 5\) , \( -13 a - 9\bigr] \)
23716.6-h2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 9 a - 14\) , \( -13 a + 9\bigr] \)
23716.6-h3	\( \bigl[1\) , \( 0\) , \( a\) , \( -179 a + 615\) , \( 1167 a - 739\bigr] \)
23716.6-h4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -361 a - 144\) , \( 787 a + 519\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph