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
deg	48	Modular degree for the optimal curve
Δ	-1216 = -1 · 26 · 19	Discriminant
Eigenvalues	2+  2 -3 -1 -3  4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,-1]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	32768/19	j-invariant
L	2.9381154123721	L(r)(E,1)/r!
Ω	2.884485985002	Real period
R	1.018592368848	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	1216q1 19a3 10944t1 30400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216d1

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 1216d1

-4	8	-3	5	-7	-19
1216q1	19a3	10944t1	30400g1	59584bn1	23104u1

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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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