Cremona's table of elliptic curves

1638 = 2 · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	1638l	Isogeny class
Conductor	1638	Conductor
∏ cp	110	Product of Tamagawa factors cp
deg	1760	Modular degree for the optimal curve
Δ	-12081678336 = -1 · 211 · 33 · 75 · 13	Discriminant
Eigenvalues	2- 3+ -3 7- -1 13+ -5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3749,89437]	[a1,a2,a3,a4,a6]
Generators	[49:-172:1]	Generators of the group modulo torsion
j	-215773279370739/447469568	j-invariant
L	3.5851042881143	L(r)(E,1)/r!
Ω	1.2707446281323	Real period
R	0.025647841779649	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	13104be1 52416bg1 1638b1 40950e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638l1

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	-	-1	+	-5	-1	1	-7	-2	1	-6	-3	-8	-2	6	-5	8	6	-11	-14	2	-14	-10

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Quadratic twists for elliptic curve 1638l1

-4	8	-3	5	-7	13
13104be1	52416bg1	1638b1	40950e1	11466bp1	21294e1

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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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