Cremona's table of elliptic curves

1976 = 2³ · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 13+ 19-	Signs for the Atkin-Lehner involutions
Class	1976b	Isogeny class
Conductor	1976	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-3952 = -1 · 24 · 13 · 19	Discriminant
Eigenvalues	2-  2  0 -2 -4 13+ -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,-7]	[a1,a2,a3,a4,a6]
Generators	[4:3:1]	Generators of the group modulo torsion
j	-4000000/247	j-invariant
L	3.7264693672912	L(r)(E,1)/r!
Ω	1.399958777584	Real period
R	1.3309211053065	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	3952a1 15808j1 17784e1 49400e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1976b1

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	0	-2	-4	+	-3	-	1	-2	3	-5	7	-3	-2	-6	1	-5	3	-12	0	-10	18	10	13

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Quadratic twists for elliptic curve 1976b1

-4	8	-3	5	-7	13	-19
3952a1	15808j1	17784e1	49400e1	96824l1	25688b1	37544g1

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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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