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	19600cp	Isogeny class
Conductor	19600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-210827008000000 = -1 · 214 · 56 · 77	Discriminant
Eigenvalues	2-  2 5+ 7-  0 -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10208,806912]	[a1,a2,a3,a4,a6]
Generators	[322:5550:1]	Generators of the group modulo torsion
j	-15625/28	j-invariant
L	7.2315577583411	L(r)(E,1)/r!
Ω	0.50236187527261	Real period
R	3.5987791442258	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	2450y1 78400il1 784j1 2800v1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600cp1

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	-4	6	2	0	-6	-4	-2	-6	8	12	-6	-6	-8	-4	0	2	-8	6	6	-10

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Quadratic twists for elliptic curve 19600cp1

-4	8	5	-7
2450y1	78400il1	784j1	2800v1

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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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