Elliptic curve isogeny class 2500.3-h over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2500.3-h
• Conductor: 2500.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2500.3-h over \(\Q(\sqrt{-11}) \)

Isogeny class 2500.3-h contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
2500.3-h1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
2500.3-h2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
2500.3-h3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
2500.3-h4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph