Elliptic curve isogeny class 10.4-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-10.4-a
• Conductor: 10.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.4-a over \(\Q(\sqrt{-31}) \)

Isogeny class 10.4-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
10.4-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 62 a + 289\) , \( -550 a + 1785\bigr] \)
10.4-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3 a - 6\) , \( -4 a + 7\bigr] \)
10.4-a3	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -1\bigr] \)
10.4-a4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 13\) , \( -7 a + 24\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 14 & 2 \\ 7 & 1 & 2 & 14 \\ 14 & 2 & 1 & 7 \\ 2 & 14 & 7 & 1 \end{array}\right)\)

Isogeny graph