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	470f	Isogeny class
Conductor	470	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	96256000 = 214 · 53 · 47	Discriminant
Eigenvalues	2- -3 5- -3 -1 -1 -8 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-117,141]	[a1,a2,a3,a4,a6]
Generators	[-9:24:1]	Generators of the group modulo torsion
j	175710096801/96256000	j-invariant
L	1.8346862508516	L(r)(E,1)/r!
Ω	1.6512381528743	Real period
R	0.026454697583517	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	3760q1 15040c1 4230j1 2350d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470f1

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	-	-3	-1	-1	-8	-5	-2	-2	-5	-4	6	6	+	2	-12	11	14	-4	-11	-4	5	14	-14

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Quadratic twists for elliptic curve 470f1

-4	8	-3	5	-7	-11	13	-47
3760q1	15040c1	4230j1	2350d1	23030s1	56870l1	79430c1	22090m1

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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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