Cremona's table of elliptic curves

3477 = 3 · 19 · 61

Field	Data	Notes
Atkin-Lehner	3+ 19- 61-	Signs for the Atkin-Lehner involutions
Class	3477a	Isogeny class
Conductor	3477	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	79319399769 = 310 · 192 · 612	Discriminant
Eigenvalues	1 3+ -2  0 -4  6  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1616,20355]	[a1,a2,a3,a4,a6]
Generators	[14730:144891:125]	Generators of the group modulo torsion
j	467162130446857/79319399769	j-invariant
L	3.1041910712808	L(r)(E,1)/r!
Ω	1.0349921860151	Real period
R	5.9984821397206	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	55632w2 10431b2 86925l2 66063h2	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3477a2

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	+	-2	0	-4	6	6	-	0	2	4	2	-2	-4	-12	10	-12	-	8	-16	-6	-4	0	-10	10

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Quadratic twists for elliptic curve 3477a2

-4	-3	5	-19
55632w2	10431b2	86925l2	66063h2

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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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