Elliptic curve isogeny class 5625.3-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-5625.3-f
• Conductor: 5625.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 5625.3-f over \(\Q(\sqrt{-11}) \)

Isogeny class 5625.3-f contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
5625.3-f1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 4 a + 6\) , \( -33\bigr] \)
5625.3-f2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -186 a - 639\) , \( 2740 a + 6012\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph