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	1968h	Isogeny class
Conductor	1968	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	-45556511932416 = -1 · 217 · 3 · 415	Discriminant
Eigenvalues	2- 3+  1  2 -2 -1 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9272560,10871040448]	[a1,a2,a3,a4,a6]
Generators	[48216:53792:27]	Generators of the group modulo torsion
j	-21525971829968662032241/11122195296	j-invariant
L	2.8097218600263	L(r)(E,1)/r!
Ω	0.38955902148049	Real period
R	0.36062851905575	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	246b2 7872bf2 5904l2 49200dl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1968h2

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	-1	-7	-5	6	0	-7	-2	-	-4	12	-6	-5	2	-3	3	9	0	-9	5	-2

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Quadratic twists for elliptic curve 1968h2

-4	8	-3	5	-7	41
246b2	7872bf2	5904l2	49200dl2	96432cl2	80688x2

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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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