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	50400eg	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	32768	Modular degree for the optimal curve
Δ	122472000 = 26 · 37 · 53 · 7	Discriminant
Eigenvalues	2- 3- 5- 7+ -6 -6  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1245,16900]	[a1,a2,a3,a4,a6]
Generators	[-25:180:1] [0:130:1]	Generators of the group modulo torsion
j	36594368/21	j-invariant
L	8.9015782081379	L(r)(E,1)/r!
Ω	1.8382849740033	Real period
R	2.421163838584	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400cb1 100800hh2 16800bb1 50400cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400eg1

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 50400eg1

-4	8	-3	5
50400cb1	100800hh2	16800bb1	50400cc1

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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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