Elliptic curve isogeny class 99937.6-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-99937.6-a
• Conductor: 99937.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 99937.6-a over \(\Q(\sqrt{-3}) \)

Isogeny class 99937.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
99937.6-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 290 a + 262\) , \( 3103 a - 4523\bigr] \)
99937.6-a2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a - 208\) , \( 253 a - 1145\bigr] \)
99937.6-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 90 a + 427\) , \( 996 a - 6173\bigr] \)
99937.6-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 8\) , \( 24 a - 32\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph