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	19680n	Isogeny class
Conductor	19680	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-141171724800000 = -1 · 212 · 38 · 55 · 412	Discriminant
Eigenvalues	2- 3+ 5+  0 -6  4 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12239,-239039]	[a1,a2,a3,a4,a6]
j	49495541909696/34465753125	j-invariant
L	1.3136804727239	L(r)(E,1)/r!
Ω	0.32842011818098	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19680h2 39360bf1 59040z2 98400t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19680n2

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	-6	4	-4	6	0	6	8	6	+	-4	12	8	4	10	-16	-6	2	-6	-12	-2	-8

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Quadratic twists for elliptic curve 19680n2

-4	8	-3	5
19680h2	39360bf1	59040z2	98400t2

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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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