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	1968g	Isogeny class
Conductor	1968	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-9068544 = -1 · 213 · 33 · 41	Discriminant
Eigenvalues	2- 3+  3 -2  6 -1  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24,-144]	[a1,a2,a3,a4,a6]
j	-389017/2214	j-invariant
L	1.9280805184572	L(r)(E,1)/r!
Ω	0.96404025922862	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	246f1 7872be1 5904v1 49200cx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1968g1

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
-	+	3	-2	6	-1	3	-5	6	0	1	2	+	-8	12	6	9	-10	13	-15	-7	4	-3	15	2

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Quadratic twists for elliptic curve 1968g1

-4	8	-3	5	-7	41
246f1	7872be1	5904v1	49200cx1	96432dd1	80688bg1

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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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