Elliptic curve isogeny class 14256.3-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14256.3-a
• Conductor: 14256.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 14256.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 14256.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14256.3-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a + 249\) , \( -1008 a + 1222\bigr] \)
14256.3-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24\) , \( 25\bigr] \)
14256.3-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 214\bigr] \)
14256.3-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a + 294\) , \( 1008 a + 214\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph