Elliptic curve isogeny class 27.2-a over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-27.2-a
• Conductor: 27.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.2-a over \(\Q(\sqrt{-47}) \)

Isogeny class 27.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 4 a - 23\) , \( 5 a + 6\bigr] \)
27.2-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 19\) , \( -a - 8\bigr] \)
27.2-a3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a + 1\) , \( -3 a + 2\bigr] \)
27.2-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a + 49\) , \( -38 a - 12\bigr] \)
27.2-a5	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 34 a - 248\) , \( 353 a - 1146\bigr] \)
27.2-a6	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a + 124\) , \( 127 a - 104\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 2 & 2 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 8 & 8 & 4 \\ 2 & 4 & 8 & 1 & 4 & 8 \\ 2 & 4 & 8 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph