Elliptic curve isogeny class 32.2-a over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-32.2-a
• Conductor: 32.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-47}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 12 \); class number \(5\).

Elliptic curves in class 32.2-a over \(\Q(\sqrt{-47}) \)

Isogeny class 32.2-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
32.2-a1	\( \bigl[a\) , \( -a\) , \( 0\) , \( a + 1\) , \( -6\bigr] \)
32.2-a2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 7 a + 9\) , \( 22 a - 94\bigr] \)
32.2-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 12 a + 162\bigr] \)
32.2-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 29\) , \( 12 a - 174\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 14 & 7 & 2 \\ 14 & 1 & 2 & 7 \\ 7 & 2 & 1 & 14 \\ 2 & 7 & 14 & 1 \end{array}\right)\)

Isogeny graph