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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-37125.7-i
• Conductor: 37125.7
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
37125.7-i1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -248 a - 705\) , \( -4412 a - 5837\bigr] \)
37125.7-i2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -358 a + 165\) , \( 2506 a - 4793\bigr] \)
37125.7-i3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -23 a - 30\) , \( -47 a - 167\bigr] \)
37125.7-i4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 12 a\) , \( -9 a - 38\bigr] \)

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