Elliptic curve isogeny class 1083.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1083.1-d
• Conductor: 1083.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1083.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 1083.1-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1083.1-d1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 245858 a - 425861\) , \( -87559214 a + 151657043\bigr] \)
1083.1-d2	\( \bigl[0\) , \( -1\) , \( a\) , \( 20\) , \( 31\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph