Cremona's table of elliptic curves

1632 = 2⁵ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17-	Signs for the Atkin-Lehner involutions
Class	1632d	Isogeny class
Conductor	1632	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-4890046464 = -1 · 212 · 35 · 173	Discriminant
Eigenvalues	2+ 3- -1  2 -5 -5 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-221,-3669]	[a1,a2,a3,a4,a6]
Generators	[73:-612:1]	Generators of the group modulo torsion
j	-292754944/1193859	j-invariant
L	3.1594660502762	L(r)(E,1)/r!
Ω	0.56422812257537	Real period
R	0.18665417549289	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	1632g1 3264f1 4896l1 40800bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1632d1

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	-5	-5	-	-7	3	2	-2	-8	-7	-5	8	4	14	6	4	8	-12	-14	0	-14	10

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Quadratic twists for elliptic curve 1632d1

-4	8	-3	5	-7	17
1632g1	3264f1	4896l1	40800bi1	79968f1	27744b1

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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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