Elliptic curve isogeny class 51492.3-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-51492.3-d
• Conductor: 51492.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 51492.3-d over \(\Q(\sqrt{-3}) \)

Isogeny class 51492.3-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
51492.3-d1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a + 24\) , \( 33 a + 9\bigr] \)
51492.3-d2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 450 a - 321\) , \( 3438 a - 609\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph