Cremona's table of elliptic curves

10504 = 2³ · 13 · 101

Field	Data	Notes
Atkin-Lehner	2- 13+ 101+	Signs for the Atkin-Lehner involutions
Class	10504a	Isogeny class
Conductor	10504	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	124801973504 = 28 · 136 · 101	Discriminant
Eigenvalues	2-  0 -2  2  6 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1271,-3910]	[a1,a2,a3,a4,a6]
j	886993420752/487507709	j-invariant
L	1.7099595109394	L(r)(E,1)/r!
Ω	0.85497975546968	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21008a2 84032j2 94536c2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10504a2

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

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Quadratic twists for elliptic curve 10504a2

-4	8	-3
21008a2	84032j2	94536c2

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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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