Elliptic curve isogeny class 39204.1-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-39204.1-a
• Conductor: 39204.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 39204.1-a over \(\Q(\sqrt{-11}) \)

Isogeny class 39204.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
39204.1-a1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -73 a + 229\) , \( -573 a - 849\bigr] \)
39204.1-a2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 39 a - 48\) , \( -162 a + 213\bigr] \)