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	50400cc	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	163840	Modular degree for the optimal curve
Δ	1913625000000 = 26 · 37 · 59 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7- -6  6  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31125,2112500]	[a1,a2,a3,a4,a6]
j	36594368/21	j-invariant
L	3.2884241307586	L(r)(E,1)/r!
Ω	0.82210603277755	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400ef1 100800im2 16800bp1 50400eg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400cc1

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

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Quadratic twists for elliptic curve 50400cc1

-4	8	-3	5
50400ef1	100800im2	16800bp1	50400eg1

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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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