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	1638i	Isogeny class
Conductor	1638	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	217326564 = 22 · 38 · 72 · 132	Discriminant
Eigenvalues	2+ 3- -2 7-  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-243,-1215]	[a1,a2,a3,a4,a6]
Generators	[-9:18:1]	Generators of the group modulo torsion
j	2181825073/298116	j-invariant
L	2.0214627052223	L(r)(E,1)/r!
Ω	1.219916466541	Real period
R	0.82852505096276	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13104bt2 52416dd2 546g2 40950dy2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638i2

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
+	-	-2	-	4	+	-6	-4	0	6	-8	10	6	4	-4	-10	-4	-6	-8	0	-10	-8	-4	6	-2

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Quadratic twists for elliptic curve 1638i2

-4	8	-3	5	-7	13
13104bt2	52416dd2	546g2	40950dy2	11466y2	21294cg2

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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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