Cremona's table of elliptic curves

19800 = 2³ · 3² · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	19800i	Isogeny class
Conductor	19800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	2756531250000 = 24 · 36 · 59 · 112	Discriminant
Eigenvalues	2+ 3- 5+  2 11-  0  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8550,293625]	[a1,a2,a3,a4,a6]
Generators	[40:125:1]	Generators of the group modulo torsion
j	379275264/15125	j-invariant
L	5.4076040310378	L(r)(E,1)/r!
Ω	0.79998568665723	Real period
R	0.84495324748147	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	39600j1 2200e1 3960s1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19800i1

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	-	0	0	-8	-8	-10	8	10	2	6	-8	14	4	10	-4	0	8	-4	10	-6	10

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Quadratic twists for elliptic curve 19800i1

-4	-3	5
39600j1	2200e1	3960s1

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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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