Elliptic curve isogeny class 640.4-c over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-640.4-c
• Conductor: 640.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 640.4-c over \(\Q(\sqrt{-31}) \)

Isogeny class 640.4-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
640.4-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a + 20\) , \( -4 a + 48\bigr] \)
640.4-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 68 a - 300\) , \( -484 a + 1456\bigr] \)
640.4-c3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -13 a - 13\) , \( -31 a + 27\bigr] \)
640.4-c4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 132 a - 213\) , \( -1054 a - 45\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph