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	10416bo	Isogeny class
Conductor	10416	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	679433761456128 = 232 · 36 · 7 · 31	Discriminant
Eigenvalues	2- 3-  2 7-  0 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-58192,-5274988]	[a1,a2,a3,a4,a6]
Generators	[-133:360:1]	Generators of the group modulo torsion
j	5320605737038033/165877383168	j-invariant
L	6.2041619231693	L(r)(E,1)/r!
Ω	0.30797255889687	Real period
R	3.3575296152965	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	1302j1 41664db1 31248cj1 72912bk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416bo1

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

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Quadratic twists for elliptic curve 10416bo1

-4	8	-3	-7
1302j1	41664db1	31248cj1	72912bk1

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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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