Elliptic curve isogeny class 3025.2-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-3025.2-c
• Conductor: 3025.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 3025.2-c over \(\Q(\sqrt{-11}) \)

Isogeny class 3025.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
3025.2-c1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 58\) , \( -30 a - 180\bigr] \)
3025.2-c2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a - 59\) , \( 26 a - 148\bigr] \)
3025.2-c3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a - 4\) , \( -7 a + 6\bigr] \)
3025.2-c4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 3\) , \( 3 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph