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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-37125.10-h
• 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-h over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
37125.10-h1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -120 a + 62\) , \( 2825 a - 5266\bigr] \)
37125.10-h2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 1005 a - 4438\) , \( 34550 a - 105166\bigr] \)
37125.10-h3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 40 a + 247\) , \( 949 a - 1107\bigr] \)
37125.10-h4	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -3805 a + 1602\) , \( 88504 a - 171102\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph