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

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-20.3-a
• Conductor: 20.3
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
20.3-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a + 40\) , \( -38 a + 48\bigr] \)
20.3-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -a\) , \( 0\bigr] \)
20.3-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( 16\bigr] \)
20.3-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a + 21\) , \( -5 a + 45\bigr] \)

Rank

Rank: \( 1 \)

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