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	-920599396352 = -1 · 227 · 193	Discriminant
Eigenvalues	2+ -1  0 -1  6 -5  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,607,45601]	[a1,a2,a3,a4,a6]
Generators	[57:512:1]	Generators of the group modulo torsion
j	94196375/3511808	j-invariant
L	2.2319890458138	L(r)(E,1)/r!
Ω	0.66843943526102	Real period
R	0.83477609491362	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	1216o2 38a1 10944l2 30400d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216b2

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 1216b2

-4	8	-3	5	-7	-19
1216o2	38a1	10944l2	30400d2	59584bg2	23104l2

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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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