Cremona's table of elliptic curves

1216 = 2⁶ · 19

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	1216b	Isogeny class
Conductor	1216	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-668503069687808 = -1 · 245 · 19	Discriminant
Eigenvalues	2+ -1  0 -1  6 -5  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5473,-1251871]	[a1,a2,a3,a4,a6]
Generators	[47215:262144:343]	Generators of the group modulo torsion
j	-69173457625/2550136832	j-invariant
L	2.2319890458138	L(r)(E,1)/r!
Ω	0.22281314508701	Real period
R	2.5043282847409	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1216o3 38a2 10944l3 30400d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216b3

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
+	-1	0	-1	6	-5	3	+	3	-9	-4	-2	0	-8	0	3	-9	10	-5	-6	-7	-10	6	-12	-10

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Quadratic twists for elliptic curve 1216b3

-4	8	-3	5	-7	-19
1216o3	38a2	10944l3	30400d3	59584bg3	23104l3

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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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