Elliptic curve isogeny class 10125.10-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-10125.10-e
• Conductor: 10125.10
• Rank: \( 0 \)

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

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

Elliptic curves in class 10125.10-e over \(\Q(\sqrt{-11}) \)

Isogeny class 10125.10-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10125.10-e1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -84 a - 377\) , \( -1107 a - 2375\bigr] \)
10125.10-e2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -66 a + 252\) , \( -515 a + 51\bigr] \)
10125.10-e3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 6 a - 62\) , \( -90 a + 172\bigr] \)
10125.10-e4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -51 a + 117\) , \( 148 a + 384\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph