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	10416s	Isogeny class
Conductor	10416	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-335978496 = -1 · 213 · 33 · 72 · 31	Discriminant
Eigenvalues	2- 3+  1 7+ -1  5 -5  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3680,87168]	[a1,a2,a3,a4,a6]
Generators	[34:14:1]	Generators of the group modulo torsion
j	-1345938541921/82026	j-invariant
L	4.0010973386497	L(r)(E,1)/r!
Ω	1.6207049363786	Real period
R	0.61718472758988	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1302p1 41664dk1 31248bn1 72912cg1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416s1

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
-	+	1	+	-1	5	-5	5	-6	6	-	-2	-6	10	-11	-6	6	13	-7	-9	-2	-1	-5	-18	-1

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Quadratic twists for elliptic curve 10416s1

-4	8	-3	-7
1302p1	41664dk1	31248bn1	72912cg1

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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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