Elliptic curve isogeny class 2500.8-j over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-2500.8-j
• Conductor: 2500.8
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-31}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 8 \); class number \(3\).

Elliptic curves in class 2500.8-j over \(\Q(\sqrt{-31}) \)

Isogeny class 2500.8-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2500.8-j1	\( \bigl[a\) , \( -a\) , \( a\) , \( 96 a + 933\) , \( -3595 a + 5846\bigr] \)
2500.8-j2	\( \bigl[a\) , \( -a\) , \( a\) , \( -29 a - 67\) , \( -95 a - 154\bigr] \)
2500.8-j3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -45 a + 42\) , \( -62 a + 436\bigr] \)
2500.8-j4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 330 a + 667\) , \( -2187 a + 15561\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph