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	1632b	Isogeny class
Conductor	1632	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-208896 = -1 · 212 · 3 · 17	Discriminant
Eigenvalues	2+ 3+ -3  2 -3  3 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,21]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	512/51	j-invariant
L	2.2079835824713	L(r)(E,1)/r!
Ω	2.4257345606852	Real period
R	0.45511648682773	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	1632k1 3264m1 4896r1 40800bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1632b1

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	2	-3	3	+	5	-3	-2	10	-12	-5	-9	8	4	-6	-10	4	0	-12	2	0	-18	-10

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Quadratic twists for elliptic curve 1632b1

-4	8	-3	5	-7	17
1632k1	3264m1	4896r1	40800bu1	79968bh1	27744m1

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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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