Elliptic curve isogeny class 700.2-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-700.2-c
• Conductor: 700.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 700.2-c over \(\Q(\sqrt{-7}) \)

Isogeny class 700.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
700.2-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 7\) , \( 6 a - 1\bigr] \)
700.2-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a - 1\) , \( -6 a + 5\bigr] \)
700.2-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \)
700.2-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \)
700.2-c5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \)
700.2-c6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph