Elliptic curve isogeny class 240.4-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-240.4-a
• Conductor: 240.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 240.4-a over \(\Q(\sqrt{-11}) \)

Isogeny class 240.4-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
240.4-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 46 a + 113\) , \( -513 a - 738\bigr] \)
240.4-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 2\) , \( 1\bigr] \)
240.4-a3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -19 a - 62\) , \( -48 a - 159\bigr] \)
240.4-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 7\) , \( 7 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 14 & 2 & 7 \\ 14 & 1 & 7 & 2 \\ 2 & 7 & 1 & 14 \\ 7 & 2 & 14 & 1 \end{array}\right)\)

Isogeny graph