Elliptic curve isogeny class 19404.2-l over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-19404.2-l
• Conductor: 19404.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 19404.2-l over \(\Q(\sqrt{-11}) \)

Isogeny class 19404.2-l contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
19404.2-l1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -823\) , \( -11611\bigr] \)
19404.2-l2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 77\) , \( 161\bigr] \)
19404.2-l3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -363\) , \( 1305\bigr] \)
19404.2-l4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -14133\) , \( -647829\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph