Elliptic curve isogeny class 225.7-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-225.7-a
• Conductor: 225.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 225.7-a over \(\Q(\sqrt{-11}) \)

Isogeny class 225.7-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
225.7-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 329 a - 22\) , \( 1370 a + 3718\bigr] \)
225.7-a2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 26 a + 48\) , \( 127 a + 116\bigr] \)
225.7-a3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( a - 2\) , \( -2 a + 2\bigr] \)
225.7-a4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 3\) , \( 4 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph