Elliptic curve isogeny class 624.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-624.1-a
• Conductor: 624.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 624.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 624.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
624.1-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 22 a - 20\) , \( -50 a + 96\bigr] \)
624.1-a2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( -2 a\bigr] \)