Elliptic curve isogeny class 9801.2-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9801.2-b
• Conductor: 9801.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 9801.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 9801.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9801.2-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 391\) , \( -1092\bigr] \)
9801.2-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -104\) , \( -102\bigr] \)
9801.2-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -59\) , \( 186\bigr] \)
9801.2-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1319\) , \( -18084\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph