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	19600dj	Isogeny class
Conductor	19600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-314703872000 = -1 · 220 · 53 · 74	Discriminant
Eigenvalues	2-  3 5- 7+  0 -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,245,-26950]	[a1,a2,a3,a4,a6]
Generators	[1245:7750:27]	Generators of the group modulo torsion
j	1323/256	j-invariant
L	8.9510101004184	L(r)(E,1)/r!
Ω	0.45583028771659	Real period
R	4.9091791076768	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	2450bc1 78400jr1 19600dk1 19600ed1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600dj1

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

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Quadratic twists for elliptic curve 19600dj1

-4	8	5	-7
2450bc1	78400jr1	19600dk1	19600ed1

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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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