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	10416f	Isogeny class
Conductor	10416	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	11999232 = 211 · 33 · 7 · 31	Discriminant
Eigenvalues	2+ 3+ -2 7- -4 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-249984,48191328]	[a1,a2,a3,a4,a6]
Generators	[293:118:1]	Generators of the group modulo torsion
j	843591384940292354/5859	j-invariant
L	3.0915696374206	L(r)(E,1)/r!
Ω	1.1078183442861	Real period
R	2.7906828347501	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	5208l3 41664ej4 31248w4 72912u4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416f3

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

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Quadratic twists for elliptic curve 10416f3

-4	8	-3	-7
5208l3	41664ej4	31248w4	72912u4

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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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