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	10416k	Isogeny class
Conductor	10416	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-39718791168 = -1 · 211 · 3 · 7 · 314	Discriminant
Eigenvalues	2+ 3- -2 7-  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,576,-7788]	[a1,a2,a3,a4,a6]
Generators	[47:354:1]	Generators of the group modulo torsion
j	10301655166/19393941	j-invariant
L	4.9768927348445	L(r)(E,1)/r!
Ω	0.60091402743416	Real period
R	4.1411021440915	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5208j4 41664cq3 31248r3 72912p3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416k4

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

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Quadratic twists for elliptic curve 10416k4

-4	8	-3	-7
5208j4	41664cq3	31248r3	72912p3

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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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