Cremona's table of elliptic curves

14504 = 2³ · 7² · 37

Field	Data	Notes
Atkin-Lehner	2- 7- 37+	Signs for the Atkin-Lehner involutions
Class	14504h	Isogeny class
Conductor	14504	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	117504	Modular degree for the optimal curve
Δ	4672071440848 = 24 · 78 · 373	Discriminant
Eigenvalues	2-  0  4 7- -4  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-827218,289586325]	[a1,a2,a3,a4,a6]
Generators	[-1050:735:1]	Generators of the group modulo torsion
j	33256413948450816/2481997	j-invariant
L	5.9568922600813	L(r)(E,1)/r!
Ω	0.58750879511535	Real period
R	5.0696196462146	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	29008d1 116032l1 2072e1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 14504h1

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

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Quadratic twists for elliptic curve 14504h1

-4	8	-7
29008d1	116032l1	2072e1

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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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