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	19600dp	Isogeny class
Conductor	19600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-205520896000 = -1 · 225 · 53 · 72	Discriminant
Eigenvalues	2-  0 5- 7- -3 -5 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-109235,13896050]	[a1,a2,a3,a4,a6]
Generators	[-185:5270:1] [169:512:1]	Generators of the group modulo torsion
j	-5745702166029/8192	j-invariant
L	7.0053760830941	L(r)(E,1)/r!
Ω	0.85131354419584	Real period
R	1.0286128023653	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2450o2 78400kc2 19600do2 19600de2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600dp2

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	-5	-2	-5	-7	-4	-2	-1	-3	2	7	-9	-4	-6	2	6	-16	-14	6	-2	-12

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Quadratic twists for elliptic curve 19600dp2

-4	8	5	-7
2450o2	78400kc2	19600do2	19600de2

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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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