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	50400ef	Isogeny class
Conductor	50400	Conductor
∏ cp	8	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	2.8755912966122	L(r)(E,1)/r!
Ω	0.35944891208842	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400cc1 100800hj2 16800bc1 50400cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400ef1

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 50400ef1

-4	8	-3	5
50400cc1	100800hj2	16800bc1	50400cb1

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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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