Elliptic curve isogeny class 7425.8-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-7425.8-b
• Conductor: 7425.8
• Rank: \( 1 \)

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

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

Elliptic curves in class 7425.8-b over \(\Q(\sqrt{-11}) \)

Isogeny class 7425.8-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7425.8-b1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 19 a + 173\) , \( 638 a - 461\bigr] \)
7425.8-b2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 69 a + 3\) , \( 144 a + 369\bigr] \)
7425.8-b3	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 4 a + 8\) , \( 17 a - 2\bigr] \)
7425.8-b4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph