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	1638j	Isogeny class
Conductor	1638	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-33965568 = -1 · 29 · 36 · 7 · 13	Discriminant
Eigenvalues	2+ 3-  0 7-  3 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,63,189]	[a1,a2,a3,a4,a6]
j	37595375/46592	j-invariant
L	1.3876537053902	L(r)(E,1)/r!
Ω	1.3876537053902	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	13104bv1 52416cj1 182b1 40950dr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638j1

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
+	-	0	-	3	-	0	2	3	0	5	-7	-3	8	3	12	-6	-1	5	-12	11	-1	-12	18	17

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Quadratic twists for elliptic curve 1638j1

-4	8	-3	5	-7	13
13104bv1	52416cj1	182b1	40950dr1	11466n1	21294cb1

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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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