Elliptic curve isogeny class 27225.9-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.9-c
• Conductor: 27225.9
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.9-c over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.9-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
27225.9-c1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 688189 a - 946261\) , \( 339338542 a - 137991185\bigr] \)
27225.9-c2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 909 a - 1251\) , \( 29132 a - 12465\bigr] \)
27225.9-c3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 29 a - 41\) , \( -238 a + 75\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph