Elliptic curve isogeny class 22500.3-n over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.3-n
• Conductor: 22500.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 22500.3-n over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.3-n contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
22500.3-n1	\( \bigl[a\) , \( a\) , \( 1\) , \( 2 a + 483\) , \( 2595 a - 578\bigr] \)
22500.3-n2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 81 a - 804\) , \( 1267 a - 8078\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph