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	19600bj	Isogeny class
Conductor	19600	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	-12358292143750000 = -1 · 24 · 58 · 711	Discriminant
Eigenvalues	2+  2 5- 7- -1 -4  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-34708,-5887713]	[a1,a2,a3,a4,a6]
Generators	[72832695823515:670510319973459:257866677125]	Generators of the group modulo torsion
j	-6288640/16807	j-invariant
L	7.0184677476215	L(r)(E,1)/r!
Ω	0.162453552922	Real period
R	21.601459683037	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	9800r1 78400kw1 19600x1 2800n1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600bj1

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	-	-	-1	-4	0	6	-3	-3	0	9	-2	-9	-6	6	8	10	1	7	2	9	12	4	-16

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Quadratic twists for elliptic curve 19600bj1

-4	8	5	-7
9800r1	78400kw1	19600x1	2800n1

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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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