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	50400bp	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-612360000000000 = -1 · 212 · 37 · 510 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,17700,772000]	[a1,a2,a3,a4,a6]
Generators	[536:12816:1]	Generators of the group modulo torsion
j	13144256/13125	j-invariant
L	6.2779653047025	L(r)(E,1)/r!
Ω	0.33890538082995	Real period
R	4.6310605111223	Regulator
r	1	Rank of the group of rational points
S	1.0000000000046	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400dj2 100800fv1 16800ca4 10080bx4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bp2

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	-2	4	0	6	-8	-6	-6	-8	-4	-2	0	10	8	0	10	4	4	10	18

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Quadratic twists for elliptic curve 50400bp2

-4	8	-3	5
50400dj2	100800fv1	16800ca4	10080bx4

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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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