Elliptic curve isogeny class 6.1-a over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-6.1-a
• Conductor: 6.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 6.1-a over \(\Q(\sqrt{-47}) \)

Isogeny class 6.1-a contains 4 curves linked by isogenies of degrees dividing 22.

Curve label	Weierstrass Coefficients
6.1-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -4 a - 5\) , \( -3 a + 14\bigr] \)
6.1-a2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -4\) , \( -a + 2\bigr] \)
6.1-a3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -49 a + 140\) , \( 173 a + 206\bigr] \)
6.1-a4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -30 a + 111\) , \( 96 a + 712\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 11 & 22 \\ 2 & 1 & 22 & 11 \\ 11 & 22 & 1 & 2 \\ 22 & 11 & 2 & 1 \end{array}\right)\)

Isogeny graph