Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 63075.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 150000 over imaginary quadratic fields with absolute discriminant 3

Note: The completeness Only modular elliptic curves are included

Results (11 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
63075.1-a1	63075.1-a	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{10} \cdot 5^{14} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓				$1$	\( 2 \cdot 7 \)	$0.120034764$	$0.488414643$	1.895497092	\( \frac{53838872576}{550546875} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( 79\) , \( -1123\bigr] \)	${y}^2+{y}={x}^{3}-{x}^{2}+79{x}-1123$
63075.1-b1	63075.1-b	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{6} \cdot 5^{2} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1[2]	$1$	\( 2 \cdot 3 \)	$1$	$2.858638960$	2.200581297	\( -\frac{160989184}{3915} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 11 a\) , \( 11\bigr] \)	${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+11a{x}+11$
63075.1-b2	63075.1-b	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{2} \cdot 5^{6} \cdot 29^{6} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1[2]	$1$	\( 2 \cdot 3^{2} \)	$1$	$0.952879653$	2.200581297	\( \frac{12747309056}{9145875} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -49 a\) , \( 80\bigr] \)	${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}-49a{x}+80$
63075.1-c1	63075.1-c	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{4} \cdot 5^{8} \cdot 29^{8} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{6} \)	$1$	$0.336809138$	1.555654772	\( -\frac{6561258219361}{3978455625} \)	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -390 a + 390\) , \( -4275\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-390a+390\right){x}-4275$
63075.1-c2	63075.1-c	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{16} \cdot 5^{2} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{4} \)	$1$	$1.347236552$	1.555654772	\( \frac{2992209121}{951345} \)	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -30 a + 30\) , \( -45\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-30a+30\right){x}-45$
63075.1-c3	63075.1-c	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{8} \cdot 5^{4} \cdot 29^{4} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{5} \)	$1$	$0.673618276$	1.555654772	\( \frac{9104453457841}{1703025} \)	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -435 a + 435\) , \( -3528\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-435a+435\right){x}-3528$
63075.1-c4	63075.1-c	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{4} \cdot 5^{2} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$0.336809138$	1.555654772	\( \frac{37286818682653441}{1305} \)	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6960 a + 6960\) , \( -224073\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-6960a+6960\right){x}-224073$
63075.1-d1	63075.1-d	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{16} \cdot 5^{8} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{6} \)	$1$	$0.621697705$	2.871498698	\( \frac{157376536199}{118918125} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 112\) , \( 263\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+112{x}+263$
63075.1-d2	63075.1-d	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{8} \cdot 5^{4} \cdot 29^{4} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{5} \)	$1$	$1.243395410$	2.871498698	\( \frac{3803721481}{1703025} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -33\) , \( 31\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-33{x}+31$
63075.1-d3	63075.1-d	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{4} \cdot 5^{2} \cdot 29^{8} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{4} \)	$1$	$0.621697705$	2.871498698	\( \frac{1888690601881}{31827645} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -258\) , \( -1589\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-258{x}-1589$
63075.1-d4	63075.1-d	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63075.1	\( 3 \cdot 5^{2} \cdot 29^{2} \)	\( 3^{4} \cdot 5^{2} \cdot 29^{2} \)	$2.45281$	$(-2a+1), (5), (29)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$2.486790820$	2.871498698	\( \frac{2305199161}{1305} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -28\) , \( 53\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-28{x}+53$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.