Elliptic curve isogeny class 6.4-a over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-6.4-a
• Conductor: 6.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 6.4-a over \(\Q(\sqrt{-47}) \)

Isogeny class 6.4-a contains 4 curves linked by isogenies of degrees dividing 22.

Curve label	Weierstrass Coefficients
6.4-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a - 3\) , \( 2\bigr] \)
6.4-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -3 a + 4\) , \( 8\bigr] \)
6.4-a3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 42 a + 104\) , \( -76 a - 264\bigr] \)
6.4-a4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 29 a + 82\) , \( -97 a + 809\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph