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	50400cj	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	945000000 = 26 · 33 · 57 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-825,9000]	[a1,a2,a3,a4,a6]
Generators	[9:48:1]	Generators of the group modulo torsion
j	2299968/35	j-invariant
L	6.4120655254081	L(r)(E,1)/r!
Ω	1.5725701965216	Real period
R	2.0387215590116	Regulator
r	1	Rank of the group of rational points
S	0.99999999999884	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400cd1 100800jq1 50400g1 10080a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400cj1

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	-2	4	6	0	-4	-6	-10	2	10	-4	4	14	6	-10	-8	-16	2	2

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Quadratic twists for elliptic curve 50400cj1

-4	8	-3	5
50400cd1	100800jq1	50400g1	10080a1

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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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