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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-15876.3-c
• 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-c over \(\Q(\sqrt{-11}) \)

Isogeny class 15876.3-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15876.3-c1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -532 a + 627\) , \( 1491 a - 12325\bigr] \)
15876.3-c2	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3682 a - 3063\) , \( -158079 a + 13325\bigr] \)
15876.3-c3	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -532 a + 447\) , \( -669 a - 13729\bigr] \)
15876.3-c4	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 2618 a + 1077\) , \( 16341 a - 132799\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph