Cremona's table of elliptic curves

473 = 11 · 43

Field	Data	Notes
Atkin-Lehner	11+ 43+	Signs for the Atkin-Lehner involutions
Class	473a	Isogeny class
Conductor	473	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	204	Modular degree for the optimal curve
Δ	-2461019 = -1 · 113 · 432	Discriminant
Eigenvalues	-2  1 -1  0 11+ -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1006,11952]	[a1,a2,a3,a4,a6]
Generators	[15:21:1]	Generators of the group modulo torsion
j	-112706583998464/2461019	j-invariant
L	1.1745884798737	L(r)(E,1)/r!
Ω	2.379719730834	Real period
R	0.24679134787483	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	7568n1 30272p1 4257e1 11825c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 473a1

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	1	-1	0	+	-2	6	-8	-1	6	-1	-3	-4	+	-8	-14	9	-4	9	-13	-16	16	-6	-7	13

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Quadratic twists for elliptic curve 473a1

-4	8	-3	5	-7	-11	13	-43
7568n1	30272p1	4257e1	11825c1	23177b1	5203a1	79937e1	20339c1

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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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