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	84474i	Isogeny class
Conductor	84474	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	314496	Modular degree for the optimal curve
Δ	-192608847750384 = -1 · 24 · 39 · 13 · 196	Discriminant
Eigenvalues	2+ 3+  2 -2  4 13-  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10356,783872]	[a1,a2,a3,a4,a6]
Generators	[356:6312:1]	Generators of the group modulo torsion
j	-132651/208	j-invariant
L	5.3817208681489	L(r)(E,1)/r!
Ω	0.50831553368232	Real period
R	5.2936812959072	Regulator
r	1	Rank of the group of rational points
S	1.0000000003721	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	84474bo1 234b1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 84474i1

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	-2	4	-	0	-	-4	-8	2	-6	6	-8	-8	12	4	10	2	-16	14	4	12	-6	10

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Quadratic twists for elliptic curve 84474i1

-3	-19
84474bo1	234b1

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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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