Elliptic curve isogeny class 10.1-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-10.1-a
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-a over \(\Q(\sqrt{-31}) \)

Isogeny class 10.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
10.1-a1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -67 a + 360\) , \( 905 a + 1396\bigr] \)
10.1-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -2 a\) , \( -a + 4\bigr] \)
10.1-a3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a - 3\) , \( 1\bigr] \)
10.1-a4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 17\) , \( 12 a - 1\bigr] \)

Rank

Rank: \( 0 \)

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