Cremona's table of elliptic curves

3648 = 2⁶ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19+	Signs for the Atkin-Lehner involutions
Class	3648b	Isogeny class
Conductor	3648	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	21576548352 = 220 · 3 · 193	Discriminant
Eigenvalues	2+ 3+  0 -4  0  4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-27393,-1735935]	[a1,a2,a3,a4,a6]
Generators	[96887:1235968:343]	Generators of the group modulo torsion
j	8671983378625/82308	j-invariant
L	2.7460827534404	L(r)(E,1)/r!
Ω	0.37109797238723	Real period
R	7.399886169615	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	3648bh3 114a3 10944o3 91200dh3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648b3

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	0	4	6	+	-6	-6	2	4	6	4	6	-6	12	-14	-8	0	14	-10	12	-6	-10

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Quadratic twists for elliptic curve 3648b3

-4	8	-3	5	-19
3648bh3	114a3	10944o3	91200dh3	69312bo3

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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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