Elliptic curve isogeny class 37125.7-g over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-37125.7-g
• Conductor: 37125.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 37125.7-g over \(\Q(\sqrt{-11}) \)

Isogeny class 37125.7-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
37125.7-g1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 23 a + 183\) , \( 3565 a - 3038\bigr] \)
37125.7-g2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -2527 a + 408\) , \( 55975 a - 79133\bigr] \)
37125.7-g3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 148 a - 192\) , \( 990 a - 263\bigr] \)
37125.7-g4	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 573 a + 5958\) , \( 113455 a - 101543\bigr] \)

Rank

Rank: \( 0 \)

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