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

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-12.1-d
• Conductor: 12.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
12.1-d1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -97 a - 663\) , \( -1164 a - 8000\bigr] \)
12.1-d2	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -10256644 a + 80673218\) , \( -2022736447430 a + 15909752478878\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph