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	19740k	Isogeny class
Conductor	19740	Conductor
∏ cp	480	Product of Tamagawa factors cp
Δ	-91688006944800000 = -1 · 28 · 32 · 55 · 78 · 472	Discriminant
Eigenvalues	2- 3+ 5- 7-  0  4  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-96180,-18516600]	[a1,a2,a3,a4,a6]
Generators	[1410:-51450:1]	Generators of the group modulo torsion
j	-384363890347590736/358156277128125	j-invariant
L	5.1530697814057	L(r)(E,1)/r!
Ω	0.13054578332417	Real period
R	0.32894396957845	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	78960cu2 59220k2 98700v2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19740k2

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

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Quadratic twists for elliptic curve 19740k2

-4	-3	5
78960cu2	59220k2	98700v2

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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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