Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	50400dx	Isogeny class
Conductor	50400	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	1680315840000000 = 212 · 37 · 57 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-32700,1136000]	[a1,a2,a3,a4,a6]
Generators	[-190:700:1] [-155:1575:1]	Generators of the group modulo torsion
j	82881856/36015	j-invariant
L	9.4780384511652	L(r)(E,1)/r!
Ω	0.42613491125126	Real period
R	1.3901170440567	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400dg3 100800nt1 16800j2 10080m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dx3

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
-	-	+	-	-4	-6	-6	4	-8	-10	4	6	-6	-4	-12	6	-4	-2	-4	0	2	-8	-12	-14	-6

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Quadratic twists for elliptic curve 50400dx3

-4	8	-3	5
50400dg3	100800nt1	16800j2	10080m3

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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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