Elliptic curve isogeny class 22500.3-g over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.3-g
• Conductor: 22500.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 22500.3-g over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.3-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
22500.3-g1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 92 a + 2044\) , \( -23015 a + 14987\bigr] \)
22500.3-g2	\( \bigl[a\) , \( a\) , \( a\) , \( -1198 a + 1272\) , \( -6324 a + 40023\bigr] \)
22500.3-g3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 442 a - 1328\) , \( 9260 a - 16865\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph