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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-7425.5-j
• 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-j over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
7425.5-j1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 21 a - 24\) , \( -307 a - 105\bigr] \)
7425.5-j2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -19 a - 39\) , \( -91 a - 24\bigr] \)
7425.5-j3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -54 a + 876\) , \( -5152 a + 1335\bigr] \)
7425.5-j4	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 736 a - 684\) , \( -9866 a - 3009\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph