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	19600cr	Isogeny class
Conductor	19600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	48384	Modular degree for the optimal curve
Δ	-50176000000000 = -1 · 219 · 59 · 72	Discriminant
Eigenvalues	2-  2 5+ 7- -3 -1 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6592,269312]	[a1,a2,a3,a4,a6]
Generators	[37:750:1]	Generators of the group modulo torsion
j	10100279/16000	j-invariant
L	6.9030074493365	L(r)(E,1)/r!
Ω	0.43185717666786	Real period
R	1.9980585660863	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	2450z1 78400io1 3920x1 19600bw1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600cr1

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	+	-	-3	-1	-6	-1	9	6	8	7	-3	2	-9	-9	0	-8	8	0	-4	10	0	-6	-10

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Quadratic twists for elliptic curve 19600cr1

-4	8	5	-7
2450z1	78400io1	3920x1	19600bw1

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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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