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
deg	256	Modular degree for the optimal curve
Δ	-137168640 = -1 · 28 · 37 · 5 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,90,436]	[a1,a2,a3,a4,a6]
Generators	[5:29:1]	Generators of the group modulo torsion
j	109902239/188160	j-invariant
L	1.573850116285	L(r)(E,1)/r!
Ω	1.2617923560486	Real period
R	0.62365654251293	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	5040bg1 20160cm1 210c1 3150bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 630d1

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 630d1

-4	8	-3	5	-7	-11	13
5040bg1	20160cm1	210c1	3150bi1	4410t1	76230dk1	106470fh1

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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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