Cremona's table of elliptic curves

630 = 2 · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	630d	Isogeny class
Conductor	630	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	252152395740 = 22 · 37 · 5 · 78	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3330,-69080]	[a1,a2,a3,a4,a6]
Generators	[-34:80:1]	Generators of the group modulo torsion
j	5602762882081/345888060	j-invariant
L	1.573850116285	L(r)(E,1)/r!
Ω	0.6308961780243	Real period
R	0.15591413562823	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5040bg4 20160cm3 210c4 3150bi3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 630d3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	+	-	-4	-2	-2	-4	8	-6	-8	-2	-2	-12	8	-6	-4	-2	12	-8	-14	0	-12	-2	10

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Quadratic twists for elliptic curve 630d3

-4	8	-3	5	-7	-11	13
5040bg4	20160cm3	210c4	3150bi3	4410t4	76230dk3	106470fh3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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