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	19600by	Isogeny class
Conductor	19600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	483840	Modular degree for the optimal curve
Δ	-7378945280000000 = -1 · 214 · 57 · 78	Discriminant
Eigenvalues	2-  3 5+ 7+  2  0  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2581075,-1596064750]	[a1,a2,a3,a4,a6]
j	-5154200289/20	j-invariant
L	5.9555147119889	L(r)(E,1)/r!
Ω	0.059555147119889	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2450c1 78400go1 3920t1 19600db1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600by1

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
-	3	+	+	2	0	4	6	3	9	4	4	-7	-5	8	2	-10	1	-9	-2	4	-10	-7	1	-14

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Quadratic twists for elliptic curve 19600by1

-4	8	5	-7
2450c1	78400go1	3920t1	19600db1

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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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