Elliptic curve isogeny class 4761.2-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4761.2-d
• Number of curves: 2
• Conductor: 4761.2
• 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 4761.2-d over \(\Q(\sqrt{3}) \)

Isogeny class 4761.2-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4761.2-d1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -369 a - 696\) , \( -6290 a - 11009\bigr] \)
4761.2-d2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -6429 a - 11061\) , \( -369269 a - 640430\bigr] \)