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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-225.7-b
• Conductor: 225.7
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
225.7-b1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -24 a + 116\) , \( -273 a - 128\bigr] \)
225.7-b2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -7 a + 10\) , \( -15 a + 17\bigr] \)
225.7-b3	\( \bigl[1\) , \( -a\) , \( a\) , \( -9 a - 11\) , \( 17 a + 8\bigr] \)
225.7-b4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 13 a - 40\) , \( -44 a + 94\bigr] \)

Rank

Rank: \( 0 \)

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