Cremona's table of elliptic curves

646 = 2 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	646d	Isogeny class
Conductor	646	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	351424 = 26 · 172 · 19	Discriminant
Eigenvalues	2-  0 -2 -2 -2 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6486,202661]	[a1,a2,a3,a4,a6]
Generators	[47:-21:1]	Generators of the group modulo torsion
j	30171143454741297/351424	j-invariant
L	2.5834562462254	L(r)(E,1)/r!
Ω	2.1316501108737	Real period
R	0.40398378593294	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	5168c2 20672a2 5814j2 16150j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646d2

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

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Quadratic twists for elliptic curve 646d2

-4	8	-3	5	-7	-11	13	17	-19
5168c2	20672a2	5814j2	16150j2	31654t2	78166c2	109174a2	10982f2	12274b2

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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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