Elliptic curve isogeny class 22500.8-w over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.8-w
• Conductor: 22500.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 22500.8-w over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.8-w contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
22500.8-w1	\( \bigl[a\) , \( 1\) , \( a\) , \( 148 a - 35\) , \( 224 a + 1845\bigr] \)
22500.8-w2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 180 a + 178\) , \( 652 a - 3067\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph