Elliptic curve isogeny class 33124.1-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-33124.1-a
• Conductor: 33124.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 33124.1-a over \(\Q(\sqrt{-11}) \)

Isogeny class 33124.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
33124.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \)
33124.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \)
33124.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \)
33124.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph