Elliptic curve isogeny class 44100.5-s over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-44100.5-s
• Conductor: 44100.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 44100.5-s over \(\Q(\sqrt{-11}) \)

Isogeny class 44100.5-s contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
44100.5-s1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -20353\) , \( -1443724\bigr] \)
44100.5-s2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \)
44100.5-s3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -578\) , \( 2756\bigr] \)
44100.5-s4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1473\) , \( -16652\bigr] \)
44100.5-s5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -4358\) , \( -109132\bigr] \)
44100.5-s6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -498\) , \( 4228\bigr] \)
44100.5-s7	\( \bigl[1\) , \( 0\) , \( 1\) , \( -21953\) , \( -1253644\bigr] \)
44100.5-s8	\( \bigl[1\) , \( 0\) , \( 1\) , \( -351233\) , \( -80149132\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\ 12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\ 12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 3 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph