Elliptic curve isogeny class 50.1-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-50.1-a
• Conductor: 50.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 50.1-a over \(\Q(\sqrt{-31}) \)

Isogeny class 50.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
50.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -609 a + 1079\) , \( -674 a + 33097\bigr] \)
50.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( a - 11\) , \( -9\bigr] \)
50.1-a3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 8\) , \( -8 a\bigr] \)
50.1-a4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -144 a - 112\) , \( 1415 a - 3512\bigr] \)

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