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	1632c	Isogeny class
Conductor	1632	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-1880064 = -1 · 212 · 33 · 17	Discriminant
Eigenvalues	2+ 3+ -1  2  1 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-141,-603]	[a1,a2,a3,a4,a6]
j	-76225024/459	j-invariant
L	1.3841465955876	L(r)(E,1)/r!
Ω	0.6920732977938	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	1632e1 3264ba1 4896k1 40800bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1632c1

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	1	-1	-	-1	5	2	2	-8	5	5	12	0	2	2	4	8	0	6	4	6	-2

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Quadratic twists for elliptic curve 1632c1

-4	8	-3	5	-7	17
1632e1	3264ba1	4896k1	40800bq1	79968w1	27744i1

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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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