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	6300c	Isogeny class
Conductor	6300	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	19289340000000 = 28 · 39 · 57 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7-  4  0 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19575,1032750]	[a1,a2,a3,a4,a6]
Generators	[-45:1350:1]	Generators of the group modulo torsion
j	10536048/245	j-invariant
L	4.2882690166184	L(r)(E,1)/r!
Ω	0.68520378870578	Real period
R	0.52153207158974	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	25200cr2 100800bg2 6300d2 1260a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300c2

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

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Quadratic twists for elliptic curve 6300c2

-4	8	-3	5	-7
25200cr2	100800bg2	6300d2	1260a2	44100m2

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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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