Elliptic curve isogeny class 4.1-c over number field \(\Q(\sqrt{273}) \)

• Base field: \(\Q(\sqrt{273}) \)
• Label: 2.2.273.1-4.1-c
• Conductor: 4.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{273}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 68 \); class number \(2\).

Elliptic curves in class 4.1-c over \(\Q(\sqrt{273}) \)

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

Curve label	Weierstrass Coefficients
4.1-c1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -5154210190 a - 40003659230\) , \( 578950785388215 a + 4493443048204343\bigr] \)
4.1-c2	\( \bigl[1\) , \( a\) , \( a\) , \( -1148661001493647 a - 8915166750217005\) , \( 72971104050763160511402 a + 566354703184017553774255\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph