Elliptic curve isogeny class 100083.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100083.1-a
• Conductor: 100083.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100083.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 100083.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
100083.1-a1	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 217 a - 166\) , \( 1103 a - 221\bigr] \)
100083.1-a2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 47 a - 96\) , \( -263 a + 357\bigr] \)
100083.1-a3	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -3 a + 4\) , \( 3 a - 1\bigr] \)
100083.1-a4	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 12 a - 11\) , \( 12 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph