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	1638g	Isogeny class
Conductor	1638	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-6501222 = -1 · 2 · 36 · 73 · 13	Discriminant
Eigenvalues	2+ 3-  4 7+ -1 13+  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,30,98]	[a1,a2,a3,a4,a6]
j	4019679/8918	j-invariant
L	1.6502334648012	L(r)(E,1)/r!
Ω	1.6502334648012	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13104cg1 52416ci1 182d1 40950ej1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638g1

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
+	-	4	+	-1	+	0	-6	7	4	7	9	3	4	-7	0	10	1	1	-16	5	11	0	6	-1

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Quadratic twists for elliptic curve 1638g1

-4	8	-3	5	-7	13
13104cg1	52416ci1	182d1	40950ej1	11466bh1	21294cs1

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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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