Elliptic curve isogeny class 1682.1-g over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1682.1-g
• Conductor: 1682.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1682.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 1682.1-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1682.1-g1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 25481 a - 44136\) , \( 2916924 a - 5052263\bigr] \)
1682.1-g2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph