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
deg	7680	Modular degree for the optimal curve
Δ	29522610432 = 28 · 312 · 7 · 31	Discriminant
Eigenvalues	2+ 3+ -2 7- -4 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1044,10368]	[a1,a2,a3,a4,a6]
Generators	[28:48:1]	Generators of the group modulo torsion
j	492040858192/115322697	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	5208l1 41664ej1 31248w1 72912u1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416f1

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 10416f1

-4	8	-3	-7
5208l1	41664ej1	31248w1	72912u1

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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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