Elliptic curve isogeny class 50.6-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-50.6-a
• Conductor: 50.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 50.6-a over \(\Q(\sqrt{-31}) \)

Isogeny class 50.6-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
50.6-a1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 605 a + 472\) , \( 1753 a + 27576\bigr] \)
50.6-a2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -11 a + 24\bigr] \)
50.6-a3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 9\) , \( 8 a - 8\bigr] \)
50.6-a4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 144 a - 256\) , \( -1415 a - 2097\bigr] \)

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