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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2500.3-a
• 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-a over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
2500.3-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \)
2500.3-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
2500.3-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \)
2500.3-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

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