Elliptic curve isogeny class 12.4-a over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-12.4-a
• Conductor: 12.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 12.4-a over \(\Q(\sqrt{-47}) \)

Isogeny class 12.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
12.4-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
12.4-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -2 a - 17\) , \( -a - 36\bigr] \)
12.4-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a + 24\) , \( -20 a + 124\bigr] \)
12.4-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 158 a - 192\) , \( -1266 a - 1090\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph