Cremona's table of elliptic curves

20800 = 2⁶ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	20800a	Isogeny class
Conductor	20800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	16640000000000 = 217 · 510 · 13	Discriminant
Eigenvalues	2+  0 5+  0  4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-56300,-5138000]	[a1,a2,a3,a4,a6]
Generators	[-101619:26873:729]	Generators of the group modulo torsion
j	9636491538/8125	j-invariant
L	5.1487612337269	L(r)(E,1)/r!
Ω	0.30995199655476	Real period
R	8.3057397451176	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	20800cf3 2600j3 4160d3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 20800a3

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	4	+	6	-4	0	2	-4	-6	-6	8	0	2	-4	10	12	-4	-14	-16	12	2	2

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Quadratic twists for elliptic curve 20800a3

-4	8	5
20800cf3	2600j3	4160d3

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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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