Elliptic curve isogeny class 105625.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-105625.2-c
• Conductor: 105625.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 105625.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 105625.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
105625.2-c1	\( \bigl[0\) , \( -a\) , \( 1\) , \( -83 a + 83\) , \( 244\bigr] \)
105625.2-c2	\( \bigl[0\) , \( -a\) , \( 1\) , \( -1333 a + 1333\) , \( -19131\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph