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

• Base field: \(\Q(\sqrt{273}) \)
• Label: 2.2.273.1-4.1-d
• 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-d over \(\Q(\sqrt{273}) \)

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

Curve label	Weierstrass Coefficients
4.1-d1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2438 a - 18900\) , \( -195660 a - 1518614\bigr] \)
4.1-d2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -543329737 a - 4216975386\) , \( -23737416272920 a - 184234533963634\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph