Elliptic curve isogeny class 45056.1-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-45056.1-e
• Conductor: 45056.1
• Rank: \( 2 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 45056.1-e over \(\Q(\sqrt{-11}) \)

Isogeny class 45056.1-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
45056.1-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -31281\) , \( 2139919\bigr] \)
45056.1-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 199\bigr] \)
45056.1-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph