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	50400ba	Isogeny class
Conductor	50400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2777664960000000 = 212 · 311 · 57 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7+  4  6  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-71442300,-232424152000]	[a1,a2,a3,a4,a6]
j	864335783029582144/59535	j-invariant
L	3.7388943563087	L(r)(E,1)/r!
Ω	0.051929088281125	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400bs4 100800mh1 16800bf3 10080cd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400ba4

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	6	0	4	6	0	-2	-2	4	-4	-6	12	-10	4	8	14	-8	12	6	14

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Quadratic twists for elliptic curve 50400ba4

-4	8	-3	5
50400bs4	100800mh1	16800bf3	10080cd2

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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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