Cremona's table of elliptic curves

6630 = 2 · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	6630j	Isogeny class
Conductor	6630	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	194959225328400 = 24 · 310 · 52 · 134 · 172	Discriminant
Eigenvalues	2+ 3- 5+  0  0 13- 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-20384,-898018]	[a1,a2,a3,a4,a6]
Generators	[-99:439:1]	Generators of the group modulo torsion
j	936615448738871929/194959225328400	j-invariant
L	3.4283123352577	L(r)(E,1)/r!
Ω	0.40541994642305	Real period
R	0.42281002273138	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	53040bk2 19890bg2 33150bj2 86190cu2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630j2

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
+	-	+	0	0	-	+	4	-8	-6	0	10	-2	0	-8	10	-4	-10	-8	4	-2	8	4	-14	-10

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Quadratic twists for elliptic curve 6630j2

-4	-3	5	13	17
53040bk2	19890bg2	33150bj2	86190cu2	112710o2

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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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