Cremona's table of elliptic curves

470 = 2 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 5+ 47+	Signs for the Atkin-Lehner involutions
Class	470a	Isogeny class
Conductor	470	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	60160 = 28 · 5 · 47	Discriminant
Eigenvalues	2+  1 5+ -1 -3 -5  2 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-44,106]	[a1,a2,a3,a4,a6]
Generators	[1:7:1]	Generators of the group modulo torsion
j	9116230969/60160	j-invariant
L	1.5542574208417	L(r)(E,1)/r!
Ω	3.5287956897084	Real period
R	0.22022490921968	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	3760h1 15040i1 4230bf1 2350m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470a1

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	-3	-5	2	-7	8	-2	-5	-4	12	8	+	-4	-10	-11	-8	0	3	10	9	-18	12

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Quadratic twists for elliptic curve 470a1

-4	8	-3	5	-7	-11	13	-47
3760h1	15040i1	4230bf1	2350m1	23030o1	56870p1	79430p1	22090g1

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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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