Elliptic curve isogeny class 1458.1-h over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1458.1-h
• Conductor: 1458.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1458.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 1458.1-h contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1458.1-h1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 6 a - 12\) , \( 20 a - 36\bigr] \)
1458.1-h2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 10\) , \( -10 a + 17\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph