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	50400bs	Isogeny class
Conductor	50400	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-5.106086013735E+21	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  6  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3918675,4553514250]	[a1,a2,a3,a4,a6]
Generators	[8090:708750:1]	Generators of the group modulo torsion
j	-1141100604753992/875529151875	j-invariant
L	6.7452086859338	L(r)(E,1)/r!
Ω	0.12523780396462	Real period
R	1.6831001882968	Regulator
r	1	Rank of the group of rational points
S	1.0000000000033	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400ba2 100800nu3 16800bz4 10080bz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bs2

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 50400bs2

-4	8	-3	5
50400ba2	100800nu3	16800bz4	10080bz4

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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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