Elliptic curve isogeny class 22500.13-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.13-c
• Conductor: 22500.13
• Rank: \( 1 \)

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

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

Elliptic curves in class 22500.13-c over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.13-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
22500.13-c1	\( \bigl[1\) , \( -a\) , \( 0\) , \( 11 a - 269\) , \( 463 a + 658\bigr] \)
22500.13-c2	\( \bigl[1\) , \( -a\) , \( 0\) , \( -189 a + 1131\) , \( 2263 a + 6058\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph