Elliptic curve isogeny class 27.3-c over number field \(\Q(\sqrt{-47}) \)

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-27.3-c
• Conductor: 27.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.3-c over \(\Q(\sqrt{-47}) \)

Isogeny class 27.3-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
27.3-c1	\( \bigl[a\) , \( -1\) , \( a\) , \( -a + 20\) , \( -8\bigr] \)
27.3-c2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -2 a - 19\) , \( -8 a - 8\bigr] \)
27.3-c3	\( \bigl[1\) , \( -1\) , \( a\) , \( a + 48\) , \( 37 a - 49\bigr] \)
27.3-c4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 3 a + 1\bigr] \)
27.3-c5	\( \bigl[a\) , \( -1\) , \( a\) , \( 4 a + 120\) , \( -128 a + 24\bigr] \)
27.3-c6	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -32 a - 214\) , \( -386 a - 1007\bigr] \)

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