Cremona's table of elliptic curves

19680 = 2⁵ · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 41-	Signs for the Atkin-Lehner involutions
Class	19680o	Isogeny class
Conductor	19680	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	8714304000 = 29 · 34 · 53 · 412	Discriminant
Eigenvalues	2- 3+ 5+  2 -2  6  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1456,21400]	[a1,a2,a3,a4,a6]
Generators	[189:2542:1]	Generators of the group modulo torsion
j	667169403272/17020125	j-invariant
L	4.4125047680549	L(r)(E,1)/r!
Ω	1.3005443233107	Real period
R	3.3928138310751	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	19680ba2 39360dc2 59040o2 98400bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19680o2

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
-	+	+	2	-2	6	0	-6	4	8	-8	-2	-	-4	-2	2	0	10	4	-12	-14	8	-12	-2	-8

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Quadratic twists for elliptic curve 19680o2

-4	8	-3	5
19680ba2	39360dc2	59040o2	98400bc2

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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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