Elliptic curve isogeny class 6976.13-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6976.13-b
• Conductor: 6976.13
• Rank: \( 1 \)

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

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

Elliptic curves in class 6976.13-b over \(\Q(\sqrt{-7}) \)

Isogeny class 6976.13-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
6976.13-b1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 491 a - 2985\) , \( 13885 a - 60787\bigr] \)
6976.13-b2	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( a + 5\) , \( -5 a + 3\bigr] \)
6976.13-b3	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -9 a - 45\) , \( 74 a - 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph