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

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-27.3-b
• Conductor: 27.3
• Rank: \( 1 \)

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

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

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

Isogeny class 27.3-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27.3-b1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -9 a + 21\) , \( -20 a - 145\bigr] \)
27.3-b2	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -5 a - 1\) , \( -10 a + 11\bigr] \)
27.3-b3	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -5 a - 55\) , \( -3 a - 170\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph