Cremona's table of elliptic curves

11704 = 2³ · 7 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 7- 11- 19+	Signs for the Atkin-Lehner involutions
Class	11704d	Isogeny class
Conductor	11704	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-1802416 = -1 · 24 · 72 · 112 · 19	Discriminant
Eigenvalues	2+ -2 -2 7- 11- -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-19,66]	[a1,a2,a3,a4,a6]
Generators	[1:7:1]	Generators of the group modulo torsion
j	-49948672/112651	j-invariant
L	2.3029330253883	L(r)(E,1)/r!
Ω	2.345582726146	Real period
R	0.49090850638473	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	23408a1 93632j1 105336bt1 81928i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11704d1

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

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Quadratic twists for elliptic curve 11704d1

-4	8	-3	-7	-11
23408a1	93632j1	105336bt1	81928i1	128744i1

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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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