Cremona's table of elliptic curves

10404 = 2² · 3² · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Class	10404i	Isogeny class
Conductor	10404	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	182784	Modular degree for the optimal curve
Δ	-4.8401249029204E+19	Discriminant
Eigenvalues	2- 3-  1  2 -3  3 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-117912,-335086252]	[a1,a2,a3,a4,a6]
Generators	[16570512935:-518459127869:12977875]	Generators of the group modulo torsion
j	-8192/2187	j-invariant
L	5.0834136816818	L(r)(E,1)/r!
Ω	0.0898566177021	Real period
R	14.143125491699	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41616cc1 3468b1 10404j1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 10404i1

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
-	-	1	2	-3	3	+	-3	-3	-6	2	10	3	-1	-2	-6	0	-10	-4	-8	-14	12	14	2	0

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Quadratic twists for elliptic curve 10404i1

-4	-3	17
41616cc1	3468b1	10404j1

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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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