Elliptic curve isogeny class 7425.5-g over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-7425.5-g
• Conductor: 7425.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 7425.5-g over \(\Q(\sqrt{-11}) \)

Isogeny class 7425.5-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7425.5-g1	\( \bigl[a\) , \( 0\) , \( a\) , \( -95 a + 147\) , \( 60 a + 938\bigr] \)
7425.5-g2	\( \bigl[a\) , \( 0\) , \( a\) , \( 5 a + 117\) , \( -294 a + 182\bigr] \)
7425.5-g3	\( \bigl[a\) , \( 0\) , \( a\) , \( -5 a + 12\) , \( -3 a + 20\bigr] \)
7425.5-g4	\( \bigl[a\) , \( 0\) , \( a\) , \( -3\) , \( -a + 5\bigr] \)

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