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	8	Product of Tamagawa factors cp
Δ	-26156861718750 = -1 · 2 · 314 · 58 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8820,404950]	[a1,a2,a3,a4,a6]
Generators	[45:290:1]	Generators of the group modulo torsion
j	-104094944089921/35880468750	j-invariant
L	1.573850116285	L(r)(E,1)/r!
Ω	0.6308961780243	Real period
R	1.2473130850259	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	5040bg6 20160cm6 210c6 3150bi6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 630d6

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 630d6

-4	8	-3	5	-7	-11	13
5040bg6	20160cm6	210c6	3150bi6	4410t6	76230dk5	106470fh5

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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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