Elliptic curve isogeny class 39204.2-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-39204.2-b
• Conductor: 39204.2
• 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 39204.2-b over \(\Q(\sqrt{-11}) \)

Isogeny class 39204.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
39204.2-b1	\( \bigl[a\) , \( a\) , \( a\) , \( -2782 a - 18726\) , \( -236524 a - 954375\bigr] \)
39204.2-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -397 a + 859\) , \( -2465 a - 9349\bigr] \)
39204.2-b3	\( \bigl[a\) , \( a\) , \( a\) , \( -142 a - 246\) , \( 1076 a - 1335\bigr] \)