Elliptic curve isogeny class 99937.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-99937.1-a
• Conductor: 99937.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 99937.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 99937.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
99937.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -262 a - 290\) , \( -3103 a - 1420\bigr] \)
99937.1-a2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 208 a - 30\) , \( -253 a - 892\bigr] \)
99937.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 5\) , \( -24 a - 8\bigr] \)
99937.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -427 a - 90\) , \( -996 a - 5177\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph