Elliptic curve isogeny class 624.2-h over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-624.2-h
• Conductor: 624.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 624.2-h over \(\Q(\sqrt{3}) \)

Isogeny class 624.2-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
624.2-h1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3\) , \( -3 a - 2\bigr] \)
624.2-h2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -20 a - 23\) , \( -71 a - 118\bigr] \)