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	6300w	Isogeny class
Conductor	6300	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-2391934099086000 = -1 · 24 · 320 · 53 · 73	Discriminant
Eigenvalues	2- 3- 5- 7+  4  6  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27660,2944825]	[a1,a2,a3,a4,a6]
j	-1605176213504/1640558367	j-invariant
L	2.5071908938342	L(r)(E,1)/r!
Ω	0.41786514897236	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	25200ft1 100800hc1 2100q1 6300be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300w1

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	2	6	2	-6	-2	4	-8	4	4	6	-4	14	-4	0	10	0	-16	-8	-10

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Quadratic twists for elliptic curve 6300w1

-4	8	-3	5	-7
25200ft1	100800hc1	2100q1	6300be1	44100dn1

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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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