Cremona's table of elliptic curves

10472 = 2³ · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 7- 11- 17-	Signs for the Atkin-Lehner involutions
Class	10472d	Isogeny class
Conductor	10472	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1014161426432 = 211 · 72 · 112 · 174	Discriminant
Eigenvalues	2+  2  0 7- 11- -4 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4488,106604]	[a1,a2,a3,a4,a6]
j	4882576639250/495196009	j-invariant
L	3.4069327935641	L(r)(E,1)/r!
Ω	0.85173319839102	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	20944b2 83776m2 94248z2 73304q2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10472d2

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

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Quadratic twists for elliptic curve 10472d2

-4	8	-3	-7	-11
20944b2	83776m2	94248z2	73304q2	115192w2

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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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