Elliptic curve isogeny class 12.1-e over number field \(\Q(\sqrt{217}) \)

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-12.1-e
• Conductor: 12.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{217}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 54 \); class number \(1\).

Elliptic curves in class 12.1-e over \(\Q(\sqrt{217}) \)

Isogeny class 12.1-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
12.1-e1	\( \bigl[1\) , \( 1\) , \( a\) , \( 15849071845 a - 124660239549\) , \( -122912772997547574 a + 966765491060639043\bigr] \)
12.1-e2	\( \bigl[1\) , \( 1\) , \( a\) , \( -1275546 a - 8757206\) , \( 2127641751 a + 14607239178\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph