Cremona's table of elliptic curves

49600 = 2⁶ · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	49600bz	Isogeny class
Conductor	49600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	77500000000000000 = 214 · 516 · 31	Discriminant
Eigenvalues	2-  0 5+ -2 -4 -4  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-120700,-9006000]	[a1,a2,a3,a4,a6]
Generators	[390:1800:1]	Generators of the group modulo torsion
j	759636032976/302734375	j-invariant
L	3.5505517444238	L(r)(E,1)/r!
Ω	0.26509732552845	Real period
R	3.3483473827202	Regulator
r	1	Rank of the group of rational points
S	1.0000000000075	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	49600c2 12400s2 9920t2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 49600bz2

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
-	0	+	-2	-4	-4	0	0	-4	-2	-	8	6	8	-6	-8	4	-2	2	0	4	0	8	6	2

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Quadratic twists for elliptic curve 49600bz2

-4	8	5
49600c2	12400s2	9920t2

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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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