Cremona's table of elliptic curves

10416 = 2⁴ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	10416bk	Isogeny class
Conductor	10416	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	3.9351964522086E+20	Discriminant
Eigenvalues	2- 3- -2 7-  2  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1836504,-82553580]	[a1,a2,a3,a4,a6]
j	167239798814188068697/96074132133998592	j-invariant
L	2.8182987019335	L(r)(E,1)/r!
Ω	0.14091493509668	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	1302a2 41664cr2 31248by2 72912bs2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416bk2

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	-	2	4	0	4	6	-2	+	6	6	-6	0	2	-4	4	0	-4	4	2	0	0	14

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Quadratic twists for elliptic curve 10416bk2

-4	8	-3	-7
1302a2	41664cr2	31248by2	72912bs2

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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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