Elliptic curve isogeny class 4.1-c over number field \(\Q(\sqrt{217}) \)

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-4.1-c
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-c over \(\Q(\sqrt{217}) \)

Isogeny class 4.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.1-c1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -7682232 a + 60424288\) , \( -18970234890 a + 149209622415\bigr] \)
4.1-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 7682232 a + 52742056\) , \( 18970234890 a + 130239387525\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph