Cremona's table of elliptic curves

1216 = 2⁶ · 19

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	1216d	Isogeny class
Conductor	1216	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-438976 = -1 · 26 · 193	Discriminant
Eigenvalues	2+  2 -3 -1 -3  4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37,-81]	[a1,a2,a3,a4,a6]
Generators	[18:69:1]	Generators of the group modulo torsion
j	-89915392/6859	j-invariant
L	2.9381154123721	L(r)(E,1)/r!
Ω	0.961495328334	Real period
R	3.0557771065441	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	1216q2 19a1 10944t2 30400g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216d2

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
+	2	-3	-1	-3	4	-3	+	0	-6	-4	-2	-6	1	-3	-12	6	1	4	6	-7	8	-12	12	8

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Quadratic twists for elliptic curve 1216d2

-4	8	-3	5	-7	-19
1216q2	19a1	10944t2	30400g2	59584bn2	23104u2

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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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