Elliptic curve isogeny class 22500.13-g over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.13-g
• Conductor: 22500.13
• Rank: \( 1 \)

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

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

Elliptic curves in class 22500.13-g over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.13-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
22500.13-g1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 1198 a + 73\) , \( 7595 a + 30106\bigr] \)
22500.13-g2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -91 a + 2136\) , \( 22922 a - 5891\bigr] \)
22500.13-g3	\( \bigl[a\) , \( -1\) , \( a\) , \( -444 a - 884\) , \( -9261 a - 7604\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph