Elliptic curve isogeny class 96100.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-96100.1-b
• Conductor: 96100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 96100.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 96100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
96100.1-b1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 28 a + 62\) , \( -324 a + 272\bigr] \)
96100.1-b2	\( \bigl[1\) , \( a\) , \( 1\) , \( -46 a + 67\) , \( -47 a + 68\bigr] \)
96100.1-b3	\( \bigl[1\) , \( a\) , \( 1\) , \( 194 a - 283\) , \( -423 a + 296\bigr] \)
96100.1-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 468 a + 1022\) , \( -19076 a + 17368\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph