Elliptic curve isogeny class 3136.1-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-3136.1-a
• Conductor: 3136.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3136.1-a over \(\Q(\sqrt{-11}) \)

Isogeny class 3136.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3136.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \)
3136.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \)
3136.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \)
3136.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph