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	10472b	Isogeny class
Conductor	10472	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	42496	Modular degree for the optimal curve
Δ	-444055568653312 = -1 · 210 · 7 · 118 · 172	Discriminant
Eigenvalues	2+ -2  0 7- 11+  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-38368,3052464]	[a1,a2,a3,a4,a6]
j	-6100178719130500/433648016263	j-invariant
L	1.038376429142	L(r)(E,1)/r!
Ω	0.51918821457099	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	20944c1 83776o1 94248bf1 73304n1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10472b1

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

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Quadratic twists for elliptic curve 10472b1

-4	8	-3	-7	-11
20944c1	83776o1	94248bf1	73304n1	115192ba1

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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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