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	646a	Isogeny class
Conductor	646	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	392768 = 26 · 17 · 192	Discriminant
Eigenvalues	2+  0  4 -2  4  6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-125,-507]	[a1,a2,a3,a4,a6]
j	216973458729/392768	j-invariant
L	1.4274356436688	L(r)(E,1)/r!
Ω	1.4274356436688	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5168d1 20672d1 5814u1 16150u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646a1

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	4	-2	4	6	+	-	-6	0	6	-4	6	-4	0	14	-4	0	4	10	10	-10	-12	14	-10

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Quadratic twists for elliptic curve 646a1

-4	8	-3	5	-7	-11	13	17	-19
5168d1	20672d1	5814u1	16150u1	31654i1	78166m1	109174i1	10982a1	12274m1

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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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