Cremona's table of elliptic curves

836 = 2² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	836a	Isogeny class
Conductor	836	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-1016576 = -1 · 28 · 11 · 192	Discriminant
Eigenvalues	2- -1  1  0 11+ -2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,-47]	[a1,a2,a3,a4,a6]
Generators	[8:19:1]	Generators of the group modulo torsion
j	-65536/3971	j-invariant
L	2.0763611931067	L(r)(E,1)/r!
Ω	1.2193960007581	Real period
R	0.85138920900836	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	3344h1 13376g1 7524g1 20900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 836a1

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	1	0	+	-2	-4	-	1	-2	-5	-3	0	2	0	-10	-3	-6	-3	5	0	-4	-4	1	-1

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Quadratic twists for elliptic curve 836a1

-4	8	-3	5	-7	-11	-19
3344h1	13376g1	7524g1	20900b1	40964e1	9196d1	15884e1

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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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