Elliptic curve isogeny class 10125.11-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-10125.11-e
• Conductor: 10125.11
• Rank: \( 0 \)

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

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

Elliptic curves in class 10125.11-e over \(\Q(\sqrt{-11}) \)

Isogeny class 10125.11-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10125.11-e1	\( \bigl[a\) , \( -a\) , \( a\) , \( -8 a - 54\) , \( 89 a + 83\bigr] \)
10125.11-e2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 66 a + 186\) , \( 515 a - 464\bigr] \)
10125.11-e3	\( \bigl[a\) , \( -a\) , \( a\) , \( 82 a - 459\) , \( 1106 a - 3481\bigr] \)
10125.11-e4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 51 a + 66\) , \( -148 a + 532\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph