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

• Base field: \(\Q(\sqrt{497}) \)
• Label: 2.2.497.1-4.1-a
• 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-a over \(\Q(\sqrt{497}) \)

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

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[1\) , \( a\) , \( 1\) , \( -4420590 a - 47064874\) , \( -12231406379 a - 130224706396\bigr] \)
4.1-a2	\( \bigl[1\) , \( a\) , \( 1\) , \( -329759135 a - 3510862509\) , \( -10883902199851 a - 115878168384348\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph