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	6300b	Isogeny class
Conductor	6300	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	661500000000 = 28 · 33 · 59 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-50175,4325750]	[a1,a2,a3,a4,a6]
j	129348709488/6125	j-invariant
L	1.7125019927945	L(r)(E,1)/r!
Ω	0.85625099639727	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200cz2 100800h2 6300a4 1260d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300b2

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

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Quadratic twists for elliptic curve 6300b2

-4	8	-3	5	-7
25200cz2	100800h2	6300a4	1260d2	44100g2

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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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