Elliptic curve isogeny class 99937.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-99937.2-a
• Conductor: 99937.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 99937.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 99937.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
99937.2-a1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 427 a + 91\) , \( -796 a + 4379\bigr] \)
99937.2-a2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -43 a - 169\) , \( 264 a + 771\bigr] \)
99937.2-a3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 262 a + 291\) , \( 2476 a + 4354\bigr] \)
99937.2-a4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -8 a - 4\) , \( -17 a + 33\bigr] \)

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