Elliptic curve isogeny class 9900.5-k over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-9900.5-k
• Conductor: 9900.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 9900.5-k over \(\Q(\sqrt{-11}) \)

Isogeny class 9900.5-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9900.5-k1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -22 a - 51\) , \( 407 a - 267\bigr] \)
9900.5-k2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 438 a + 2689\) , \( -30961 a + 41289\bigr] \)
9900.5-k3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -22 a + 829\) , \( 4807 a - 1323\bigr] \)
9900.5-k4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -482 a + 13049\) , \( 332735 a - 115039\bigr] \)

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