Elliptic curve isogeny class 4.1-c over number field \(\Q(\sqrt{497}) \)

• Base field: \(\Q(\sqrt{497}) \)
• Label: 2.2.497.1-4.1-c
• Conductor: 4.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{497}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 124 \); class number \(1\).

Elliptic curves in class 4.1-c over \(\Q(\sqrt{497}) \)

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

Curve label	Weierstrass Coefficients
4.1-c1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 4420590 a - 51485464\) , \( 12231406379 a - 142456112775\bigr] \)
4.1-c2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 329759135 a - 3840621644\) , \( 10883902199851 a - 126762070584199\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph