Elliptic curve isogeny class 100048.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100048.3-b
• Conductor: 100048.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 100048.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 100048.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100048.3-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 82 a - 51\) , \( -237 a + 6\bigr] \)
100048.3-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 7 a - 11\) , \( 8 a - 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph