Elliptic curve isogeny class 30976.14-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30976.14-b
• Conductor: 30976.14
• Rank: \( 1 \)

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

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

Elliptic curves in class 30976.14-b over \(\Q(\sqrt{-7}) \)

Isogeny class 30976.14-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
30976.14-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -125125\) , \( 16994227\bigr] \)
30976.14-b2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 1427\bigr] \)
30976.14-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph