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	50400co	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-120558375000000000 = -1 · 29 · 39 · 512 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 -2  8  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-189675,-35916750]	[a1,a2,a3,a4,a6]
Generators	[15732485990:-200604668750:26730899]	Generators of the group modulo torsion
j	-4792616856/765625	j-invariant
L	6.403704724092	L(r)(E,1)/r!
Ω	0.11338899447448	Real period
R	14.118885068566	Regulator
r	1	Rank of the group of rational points
S	0.99999999999843	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400cg2 100800jw2 50400k2 10080e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400co2

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	-2	8	6	4	2	-4	8	-10	-10	-10	2	4	4	-10	-6	-6	8	-8	6	14

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Quadratic twists for elliptic curve 50400co2

-4	8	-3	5
50400cg2	100800jw2	50400k2	10080e2

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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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