Elliptic curve isogeny class 34969.1-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-34969.1-c
• Conductor: 34969.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 34969.1-c over \(\Q(\sqrt{-11}) \)

Isogeny class 34969.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
34969.1-c1	\( \bigl[0\) , \( -1\) , \( 1\) , \( 110 a + 147\) , \( -506 a + 1726\bigr] \)
34969.1-c2	\( \bigl[0\) , \( -1\) , \( 1\) , \( -110 a + 257\) , \( 506 a + 1220\bigr] \)
34969.1-c3	\( \bigl[0\) , \( -1\) , \( 1\) , \( 37\) , \( 76\bigr] \)