Cremona's table of elliptic curves

19740 = 2² · 3 · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7- 47+	Signs for the Atkin-Lehner involutions
Class	19740w	Isogeny class
Conductor	19740	Conductor
∏ cp	648	Product of Tamagawa factors cp
Δ	-1341912996795168000 = -1 · 28 · 318 · 53 · 72 · 472	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-275700,78717348]	[a1,a2,a3,a4,a6]
Generators	[-552:7938:1]	Generators of the group modulo torsion
j	-9053064620747380816/5241847643731125	j-invariant
L	6.8396975208394	L(r)(E,1)/r!
Ω	0.251282803951	Real period
R	1.5121734938786	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	78960bz2 59220p2 98700d2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19740w2

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

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Quadratic twists for elliptic curve 19740w2

-4	-3	5
78960bz2	59220p2	98700d2

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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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