Cremona's table of elliptic curves

84474 = 2 · 3² · 13 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 19-	Signs for the Atkin-Lehner involutions
Class	84474bn	Isogeny class
Conductor	84474	Conductor
∏ cp	104	Product of Tamagawa factors cp
deg	3144960	Modular degree for the optimal curve
Δ	-1873698870915735552 = -1 · 213 · 39 · 13 · 197	Discriminant
Eigenvalues	2- 3+  2 -5 -5 13- -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1155629,482965525]	[a1,a2,a3,a4,a6]
Generators	[575:-3176:1] [385:9554:1]	Generators of the group modulo torsion
j	-184317154371/2023424	j-invariant
L	15.508285175397	L(r)(E,1)/r!
Ω	0.26466170596628	Real period
R	0.56342917514728	Regulator
r	2	Rank of the group of rational points
S	1.0000000000058	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	84474k1 4446c1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 84474bn1

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	-5	-5	-	-4	-	-5	-8	-6	8	-4	-9	-2	-6	-6	-10	-3	1	2	-5	0	-12	-10

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Quadratic twists for elliptic curve 84474bn1

-3	-19
84474k1	4446c1

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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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