Elliptic curve isogeny class 20.3-b over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-20.3-b
• Conductor: 20.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 20.3-b over \(\Q(\sqrt{-31}) \)

Isogeny class 20.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.3-b1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 78 a - 963\) , \( -1718 a + 12067\bigr] \)
20.3-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( 3 a + 29\) , \( 16 a - 58\bigr] \)
20.3-b3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 3\) , \( -6 a + 35\bigr] \)
20.3-b4	\( \bigl[a\) , \( 0\) , \( a\) , \( 68 a - 171\) , \( 452 a - 346\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph