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	1638o	Isogeny class
Conductor	1638	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-6368544 = -1 · 25 · 37 · 7 · 13	Discriminant
Eigenvalues	2- 3- -1 7+ -3 13+ -5  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-68,263]	[a1,a2,a3,a4,a6]
Generators	[9:-23:1]	Generators of the group modulo torsion
j	-47045881/8736	j-invariant
L	3.7345773807799	L(r)(E,1)/r!
Ω	2.2858035437784	Real period
R	0.081690690150186	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	13104cb1 52416bx1 546b1 40950bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638o1

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
-	-	-1	+	-3	+	-5	1	-3	-5	4	-5	8	-1	-8	-6	0	13	-10	-8	-15	6	2	2	-2

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Quadratic twists for elliptic curve 1638o1

-4	8	-3	5	-7	13
13104cb1	52416bx1	546b1	40950bq1	11466cj1	21294be1

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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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