Elliptic curve isogeny class 2116.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-2116.5-c
• Conductor: 2116.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 2116.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 2116.5-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2116.5-c1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -7 a + 5\) , \( -6 a + 18\bigr] \)
2116.5-c2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 3 a - 25\) , \( -6 a + 66\bigr] \)
2116.5-c3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 53 a - 30\) , \( 103 a - 36\bigr] \)
2116.5-c4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 733 a - 470\) , \( 7319 a + 2764\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph