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	19600ct	Isogeny class
Conductor	19600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-4519603984000000000 = -1 · 213 · 59 · 710	Discriminant
Eigenvalues	2-  2 5+ 7- -3  5  6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9624008,-11488889488]	[a1,a2,a3,a4,a6]
Generators	[12910054636292:1189905191454216:1341919727]	Generators of the group modulo torsion
j	-5452947409/250	j-invariant
L	7.4724582664534	L(r)(E,1)/r!
Ω	0.042857749963118	Real period
R	21.794361209128	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	2450h2 78400iq2 3920bg2 19600bx2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600ct2

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	5	6	-1	3	-6	-4	-11	-3	-10	-3	-3	0	4	-4	-12	-4	10	12	-6	14

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Quadratic twists for elliptic curve 19600ct2

-4	8	5	-7
2450h2	78400iq2	3920bg2	19600bx2

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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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