Cremona's table of elliptic curves

6300 = 2² · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	6300k	Isogeny class
Conductor	6300	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2930238281250000 = 24 · 37 · 512 · 73	Discriminant
Eigenvalues	2- 3- 5+ 7+ -6  4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-67800,6276125]	[a1,a2,a3,a4,a6]
Generators	[-205:3400:1]	Generators of the group modulo torsion
j	189123395584/16078125	j-invariant
L	3.8422423283707	L(r)(E,1)/r!
Ω	0.44056209940781	Real period
R	4.3606137858151	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200et3 100800ei3 2100b3 1260j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300k3

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	4	6	2	0	-6	-10	-2	6	4	0	-12	0	14	4	-6	4	-16	-12	-6	16

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Quadratic twists for elliptic curve 6300k3

-4	8	-3	5	-7
25200et3	100800ei3	2100b3	1260j3	44100cp3

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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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