Elliptic curve isogeny class 1600.1-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-1600.1-a
• Conductor: 1600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1600.1-a over \(\Q(\sqrt{-31}) \)

Isogeny class 1600.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
1600.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5318 a - 3809\) , \( -194953 a - 321409\bigr] \)
1600.1-a2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -42 a + 31\) , \( -121 a + 383\bigr] \)
1600.1-a3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a - 77\) , \( 34 a - 267\bigr] \)
1600.1-a4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 900 a + 2043\) , \( 3603 a + 93997\bigr] \)

Rank

Rank: \( 1 \)

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