Elliptic curve isogeny class 6.2-h over number field \(\Q(\sqrt{457}) \)

• Base field: \(\Q(\sqrt{457}) \)
• Label: 2.2.457.1-6.2-h
• Conductor: 6.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{457}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 114 \); class number \(1\).

Elliptic curves in class 6.2-h over \(\Q(\sqrt{457}) \)

Isogeny class 6.2-h contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
6.2-h1	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1007173847636 a - 11269045759749\) , \( 1798816917659029249 a - 20126565246743730767\bigr] \)
6.2-h2	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -38401432366532240535 a - 391263713933771222454\) , \( -417760201976105416924764390371 a - 4256466441115040080323818933150\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph