Cremona's table of elliptic curves

19404 = 2² · 3² · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	19404g	Isogeny class
Conductor	19404	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-139793288198256 = -1 · 24 · 39 · 79 · 11	Discriminant
Eigenvalues	2- 3+ -3 7- 11- -5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-30429,2120769]	[a1,a2,a3,a4,a6]
Generators	[-48:1863:1] [112:343:1]	Generators of the group modulo torsion
j	-84098304/3773	j-invariant
L	6.3864935938334	L(r)(E,1)/r!
Ω	0.57634400264816	Real period
R	1.3851305740343	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	77616dm2 19404c1 2772d2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 19404g2

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
-	+	-3	-	-	-5	-6	1	0	-9	-8	-7	-6	-10	-3	6	9	-2	-13	6	-11	-10	6	-6	10

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Quadratic twists for elliptic curve 19404g2

-4	-3	-7
77616dm2	19404c1	2772d2

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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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