Cremona's table of elliptic curves

1328 = 2⁴ · 83

Field	Data	Notes
Atkin-Lehner	2+ 83-	Signs for the Atkin-Lehner involutions
Class	1328c	Isogeny class
Conductor	1328	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-21248 = -1 · 28 · 83	Discriminant
Eigenvalues	2+  3 -4  5  3 -4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,-10]	[a1,a2,a3,a4,a6]
j	-148176/83	j-invariant
L	2.8607948551611	L(r)(E,1)/r!
Ω	1.4303974275806	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	664a1 5312l1 11952c1 33200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1328c1

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	-4	5	3	-4	-3	4	0	5	5	-3	-2	4	2	-6	-7	-15	6	6	-10	8	-	-12	16

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Quadratic twists for elliptic curve 1328c1

-4	8	-3	5	-7	-83
664a1	5312l1	11952c1	33200c1	65072c1	110224e1

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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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