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	1638a	Isogeny class
Conductor	1638	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1632	Modular degree for the optimal curve
Δ	-234770006016 = -1 · 217 · 39 · 7 · 13	Discriminant
Eigenvalues	2+ 3+  1 7+  5 13-  1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,741,21797]	[a1,a2,a3,a4,a6]
j	2284322013/11927552	j-invariant
L	1.4272762311308	L(r)(E,1)/r!
Ω	0.71363811556538	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	13104bl1 52416e1 1638k1 40950de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638a1

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	+	5	-	1	-1	5	1	-6	7	2	1	0	6	6	-7	-8	10	9	2	2	-6	14

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Quadratic twists for elliptic curve 1638a1

-4	8	-3	5	-7	13
13104bl1	52416e1	1638k1	40950de1	11466d1	21294bx1

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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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