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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.3-e
• 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-e over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
22500.3-e1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -59 a + 19\) , \( -195 a + 309\bigr] \)
22500.3-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 90 a - 3\) , \( 147 a + 574\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph