Cremona's table of elliptic curves

1216 = 2⁶ · 19

Field	Data	Notes
Atkin-Lehner	2+ 19-	Signs for the Atkin-Lehner involutions
Class	1216g	Isogeny class
Conductor	1216	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-311296 = -1 · 214 · 19	Discriminant
Eigenvalues	2+  2  1 -3  3  4  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,29]	[a1,a2,a3,a4,a6]
j	-1024/19	j-invariant
L	2.5778616440777	L(r)(E,1)/r!
Ω	2.5778616440777	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1216l1 152a1 10944bc1 30400p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1216g1

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	1	-3	3	4	5	-	0	-2	8	10	6	7	-9	8	-14	5	0	-6	-15	-4	-4	0	16

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Quadratic twists for elliptic curve 1216g1

-4	8	-3	5	-7	-19
1216l1	152a1	10944bc1	30400p1	59584v1	23104t1

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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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