Elliptic curve isogeny class 746.2-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-746.2-b
• Number of curves: 2
• Conductor: 746.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 746.2-b over \(\Q(\sqrt{3}) \)

Isogeny class 746.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
746.2-b1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2 a - 1\) , \( -3\bigr] \)
746.2-b2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2 a + 4\) , \( -32 a + 44\bigr] \)