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	1968i	Isogeny class
Conductor	1968	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	24182784 = 216 · 32 · 41	Discriminant
Eigenvalues	2- 3+ -2 -4  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-144,-576]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	81182737/5904	j-invariant
L	2.1843327723103	L(r)(E,1)/r!
Ω	1.3837153324861	Real period
R	0.7892999091026	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	246e1 7872bi1 5904m1 49200dr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1968i1

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	-4	4	2	2	4	0	-6	8	-2	-	-4	-12	-6	4	-10	-12	12	-6	-12	-12	2	10

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Quadratic twists for elliptic curve 1968i1

-4	8	-3	5	-7	41
246e1	7872bi1	5904m1	49200dr1	96432cm1	80688bd1

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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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