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	1632a	Isogeny class
Conductor	1632	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-970818048 = -1 · 29 · 38 · 172	Discriminant
Eigenvalues	2+ 3+  0  2  0 -6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-448,-3800]	[a1,a2,a3,a4,a6]
Generators	[1050:11815:8]	Generators of the group modulo torsion
j	-19465109000/1896129	j-invariant
L	2.5458912278648	L(r)(E,1)/r!
Ω	0.51591055575598	Real period
R	4.9347531262162	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	1632i2 3264k2 4896p2 40800bt2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1632a2

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
+	+	0	2	0	-6	+	-4	6	-8	-2	12	-2	12	-4	-14	-12	-4	4	-6	-6	14	-12	6	-10

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Quadratic twists for elliptic curve 1632a2

-4	8	-3	5	-7	17
1632i2	3264k2	4896p2	40800bt2	79968ba2	27744h2

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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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