Elliptic curve isogeny class 27225.3-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.3-e
• Conductor: 27225.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.3-e over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.3-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
27225.3-e1	\( \bigl[0\) , \( a\) , \( 1\) , \( 602166 a + 516141\) , \( -81612670 a + 587936165\bigr] \)
27225.3-e2	\( \bigl[0\) , \( a\) , \( 1\) , \( 796 a + 681\) , \( -6640 a + 50405\bigr] \)
27225.3-e3	\( \bigl[0\) , \( a\) , \( 1\) , \( 26 a + 21\) , \( 70 a - 415\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph