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

• Base field: \(\Q(\sqrt{-47}) \)
• Label: 2.0.47.1-27.2-b
• Conductor: 27.2
• Rank: \( 1 \)

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

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

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

Isogeny class 27.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27.2-b1	\( \bigl[0\) , \( a\) , \( a + 1\) , \( 5 a - 6\) , \( 9 a + 1\bigr] \)
27.2-b2	\( \bigl[0\) , \( a\) , \( 1\) , \( 9 a + 12\) , \( 20 a - 165\bigr] \)
27.2-b3	\( \bigl[0\) , \( a\) , \( a\) , \( 5 a - 60\) , \( 2 a - 172\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph