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	10472a	Isogeny class
Conductor	10472	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	6585463808 = 210 · 7 · 11 · 174	Discriminant
Eigenvalues	2+  0  2 7+ 11- -6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1739,27638]	[a1,a2,a3,a4,a6]
j	567966213252/6431117	j-invariant
L	1.3399581531744	L(r)(E,1)/r!
Ω	1.3399581531744	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	20944d3 83776a3 94248u3 73304s3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10472a4

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

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Quadratic twists for elliptic curve 10472a4

-4	8	-3	-7	-11
20944d3	83776a3	94248u3	73304s3	115192bi3

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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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