Elliptic curve isogeny class 74529.6-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-74529.6-e
• Conductor: 74529.6
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 2 & 4 & 6 & 12 \\ 3 & 1 & 12 & 4 & 6 & 12 & 2 & 4 \\ 4 & 12 & 1 & 12 & 2 & 4 & 6 & 3 \\ 12 & 4 & 12 & 1 & 6 & 3 & 2 & 4 \\ 2 & 6 & 2 & 6 & 1 & 2 & 3 & 6 \\ 4 & 12 & 4 & 3 & 2 & 1 & 6 & 12 \\ 6 & 2 & 6 & 2 & 3 & 6 & 1 & 2 \\ 12 & 4 & 3 & 4 & 6 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 74529.6-e over \(\Q(\sqrt{-3}) \)

Isogeny class 74529.6-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
74529.6-e1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4453 a - 2192\) , \( 74799 a + 27849\bigr] \)
74529.6-e2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 300 a - 27\) , \( -6438 a + 52\bigr] \)
74529.6-e3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -287 a - 2\) , \( 4263 a + 3141\bigr] \)
74529.6-e4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -45 a - 12\) , \( 126 a - 35\bigr] \)
74529.6-e5	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 283 a - 137\) , \( 1185 a + 321\bigr] \)
74529.6-e6	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 58 a - 17\) , \( -33 a - 111\bigr] \)
74529.6-e7	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -165 a - 117\) , \( -1311 a - 215\bigr] \)
74529.6-e8	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -2550 a - 1887\) , \( -85452 a - 13442\bigr] \)