Elliptic curve isogeny class 50625.1-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50625.1-g
• Conductor: 50625.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 50625.1-g over \(\Q(\sqrt{-3}) \)

Isogeny class 50625.1-g contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
50625.1-g1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -1618 a + 305\) , \( 24281 a - 17740\bigr] \)
50625.1-g2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 1616 a - 1312\) , \( -24282 a + 6541\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph