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
deg	384	Modular degree for the optimal curve
Δ	-39845888 = -1 · 221 · 19	Discriminant
Eigenvalues	2+ -1  0 -1  6 -5  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-993,12385]	[a1,a2,a3,a4,a6]
Generators	[9:64:1]	Generators of the group modulo torsion
j	-413493625/152	j-invariant
L	2.2319890458138	L(r)(E,1)/r!
Ω	2.0053183057831	Real period
R	0.27825869830454	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	1216o1 38a3 10944l1 30400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216b1

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 1216b1

-4	8	-3	5	-7	-19
1216o1	38a3	10944l1	30400d1	59584bg1	23104l1

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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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