Cremona's table of elliptic curves

1968 = 2⁴ · 3 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 41-	Signs for the Atkin-Lehner involutions
Class	1968b	Isogeny class
Conductor	1968	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-1652742144 = -1 · 211 · 39 · 41	Discriminant
Eigenvalues	2+ 3- -1  2 -2 -3 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,184,-1644]	[a1,a2,a3,a4,a6]
Generators	[10:36:1]	Generators of the group modulo torsion
j	334568302/807003	j-invariant
L	3.3846520210868	L(r)(E,1)/r!
Ω	0.77420435625457	Real period
R	0.12143836564249	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	984a1 7872v1 5904c1 49200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1968b1

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	2	-2	-3	-3	-7	-6	0	-7	10	-	12	-12	10	-11	10	7	-1	1	-4	-15	1	-18

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Quadratic twists for elliptic curve 1968b1

-4	8	-3	5	-7	41
984a1	7872v1	5904c1	49200i1	96432a1	80688a1

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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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