Elliptic curve isogeny class 15876.3-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-15876.3-f
• Conductor: 15876.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 15876.3-f over \(\Q(\sqrt{-11}) \)

Isogeny class 15876.3-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
15876.3-f1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \)
15876.3-f2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \)
15876.3-f3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \)
15876.3-f4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \)
15876.3-f5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -756\) , \( -7808\bigr] \)
15876.3-f6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -12096\) , \( -509036\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph