Elliptic curve isogeny class 20.4-b over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-20.4-b
• Conductor: 20.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 20.4-b over \(\Q(\sqrt{-31}) \)

Isogeny class 20.4-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.4-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( -80 a - 883\) , \( 1717 a + 10350\bigr] \)
20.4-b2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -70 a - 103\) , \( -453 a + 106\bigr] \)
20.4-b3	\( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( 5 a + 30\bigr] \)
20.4-b4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a + 32\) , \( -17 a - 42\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph