Elliptic curve isogeny class 1620.3-b over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-1620.3-b
• Conductor: 1620.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 1620.3-b over \(\Q(\sqrt{-31}) \)

Isogeny class 1620.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1620.3-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 36 a + 336\) , \( 580 a - 1620\bigr] \)
1620.3-b2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a - 24\) , \( 49 a + 36\bigr] \)
1620.3-b3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -18 a + 17\) , \( 22 a - 75\bigr] \)
1620.3-b4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 117 a + 242\) , \( 472 a - 3693\bigr] \)

Rank

Rank: \( 0 \)

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