Cremona's table of elliptic curves

1634 = 2 · 19 · 43

Field	Data	Notes
Atkin-Lehner	2+ 19- 43-	Signs for the Atkin-Lehner involutions
Class	1634a	Isogeny class
Conductor	1634	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-52288 = -1 · 26 · 19 · 43	Discriminant
Eigenvalues	2+ -2 -2  1  0 -2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,8,6]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	67419143/52288	j-invariant
L	1.3736197512807	L(r)(E,1)/r!
Ω	2.2793030533265	Real period
R	0.30132450998036	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	13072d1 52288a1 14706v1 40850i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1634a1

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
+	-2	-2	1	0	-2	3	-	4	5	-8	1	2	-	4	0	7	12	-1	-10	-8	-9	2	7	-8

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Quadratic twists for elliptic curve 1634a1

-4	8	-3	5	-7	-19	-43
13072d1	52288a1	14706v1	40850i1	80066a1	31046l1	70262g1

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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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