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
deg	114048	Modular degree for the optimal curve
Δ	555291875250000 = 24 · 39 · 56 · 74 · 47	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-306325,65144348]	[a1,a2,a3,a4,a6]
Generators	[-559:7875:1]	Generators of the group modulo torsion
j	198679232562180653056/34705742203125	j-invariant
L	6.8396975208394	L(r)(E,1)/r!
Ω	0.50256560790201	Real period
R	0.75608674693928	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	78960bz1 59220p1 98700d1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19740w1

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 19740w1

-4	-3	5
78960bz1	59220p1	98700d1

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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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