Elliptic curve isogeny class 14.2-a over number field \(\Q(\sqrt{-31}) \)

• Base field: \(\Q(\sqrt{-31}) \)
• Label: 2.0.31.1-14.2-a
• Conductor: 14.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 14.2-a over \(\Q(\sqrt{-31}) \)

Isogeny class 14.2-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
14.2-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a + 29\) , \( -24 a - 42\bigr] \)
14.2-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a - 266\) , \( 467 a + 1516\bigr] \)
14.2-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
14.2-a4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( -a - 38\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph