Elliptic curve isogeny class 3564.3-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-3564.3-e
• Conductor: 3564.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 3564.3-e over \(\Q(\sqrt{-11}) \)

Isogeny class 3564.3-e contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
3564.3-e1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -90495\) , \( 10538343\bigr] \)
3564.3-e2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 1035\) , \( -15147\bigr] \)
3564.3-e3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -405\) , \( -2187\bigr] \)
3564.3-e4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -90585\) , \( 10516473\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph