Elliptic curve isogeny class 32.5-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-32.5-a
• Conductor: 32.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 32.5-a over \(\Q(\sqrt{-31}) \)

Isogeny class 32.5-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
32.5-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -4 a + 34\) , \( 19 a - 4\bigr] \)
32.5-a2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 6\) , \( -a + 4\bigr] \)
32.5-a3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( 4 a - 16\bigr] \)
32.5-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( 4 a + 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph