Cremona's table of elliptic curves

81600 = 2⁶ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	81600dk	Isogeny class
Conductor	81600	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	5772971520000000 = 215 · 33 · 57 · 174	Discriminant
Eigenvalues	2+ 3- 5+  0  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-153633,-22939137]	[a1,a2,a3,a4,a6]
Generators	[603:10200:1]	Generators of the group modulo torsion
j	783267508232/11275335	j-invariant
L	8.0390887463564	L(r)(E,1)/r!
Ω	0.2413552575772	Real period
R	0.69391906832084	Regulator
r	1	Rank of the group of rational points
S	1.0000000004585	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	81600t4 40800f3 16320k3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 81600dk4

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	0	-2	-	4	-4	-2	0	-2	6	-8	-8	6	4	6	8	-16	10	8	-12	10	-6

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Quadratic twists for elliptic curve 81600dk4

-4	8	5
81600t4	40800f3	16320k3

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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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