Cremona's table of elliptic curves

19600 = 2⁴ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	19600cm	Isogeny class
Conductor	19600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	290304	Modular degree for the optimal curve
Δ	-141237624500000000 = -1 · 28 · 59 · 710	Discriminant
Eigenvalues	2- -1 5+ 7- -6  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1220508,519712012]	[a1,a2,a3,a4,a6]
Generators	[657:1000:1]	Generators of the group modulo torsion
j	-177953104/125	j-invariant
L	3.4794505018805	L(r)(E,1)/r!
Ω	0.32390133424043	Real period
R	2.6855790128498	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	4900h1 78400hq1 3920be1 19600bu1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600cm1

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	+	-	-6	2	-6	8	3	3	2	-8	3	5	0	-12	0	1	-7	0	-10	4	-3	3	-10

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Quadratic twists for elliptic curve 19600cm1

-4	8	5	-7
4900h1	78400hq1	3920be1	19600bu1

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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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