Cremona's table of elliptic curves

29640 = 2³ · 3 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13- 19+	Signs for the Atkin-Lehner involutions
Class	29640c	Isogeny class
Conductor	29640	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6528	Modular degree for the optimal curve
Δ	-18021120 = -1 · 28 · 3 · 5 · 13 · 192	Discriminant
Eigenvalues	2+ 3+ 5+ -1 -3 13- -7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,39,-195]	[a1,a2,a3,a4,a6]
Generators	[11:-38:1] [5:10:1]	Generators of the group modulo torsion
j	24974336/70395	j-invariant
L	6.6064037365978	L(r)(E,1)/r!
Ω	1.1208345955689	Real period
R	0.736772821199	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59280r1 88920bs1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 29640c1

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
+	+	+	-1	-3	-	-7	+	-3	0	-10	3	-3	6	-2	-9	-4	1	-4	-1	-14	-11	-6	15	-11

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Quadratic twists for elliptic curve 29640c1

-4	-3
59280r1	88920bs1

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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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