Elliptic curve isogeny class 33124.5-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-33124.5-c
• Conductor: 33124.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 33124.5-c over \(\Q(\sqrt{-3}) \)

Isogeny class 33124.5-c contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
33124.5-c1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -15663 a + 15663\) , \( -755809\bigr] \)
33124.5-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -193 a + 193\) , \( -1055\bigr] \)
33124.5-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -23 a + 1093\) , \( 16670 a - 8609\bigr] \)
33124.5-c4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1093 a + 23\) , \( -16670 a + 8061\bigr] \)
33124.5-c5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7 a - 7\) , \( -7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph