Elliptic curve isogeny class 37125.10-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-37125.10-c
• Conductor: 37125.10
• Rank: \( 1 \)

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

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

Elliptic curves in class 37125.10-c over \(\Q(\sqrt{-11}) \)

Isogeny class 37125.10-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
37125.10-c1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 537 a - 505\) , \( -6338 a - 972\bigr] \)
37125.10-c2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 77 a - 615\) , \( 1010 a - 5554\bigr] \)
37125.10-c3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 27 a - 40\) , \( -110 a - 99\bigr] \)
37125.10-c4	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -8 a + 25\) , \( -13 a - 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph