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	10416y	Isogeny class
Conductor	10416	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	476625494016 = 213 · 32 · 7 · 314	Discriminant
Eigenvalues	2- 3+  2 7- -4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11072,-443520]	[a1,a2,a3,a4,a6]
Generators	[162:1410:1]	Generators of the group modulo torsion
j	36650611029313/116363646	j-invariant
L	4.3862075634764	L(r)(E,1)/r!
Ω	0.46550319395832	Real period
R	4.7112539939619	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	1302n3 41664eb4 31248cb4 72912dc4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416y3

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

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Quadratic twists for elliptic curve 10416y3

-4	8	-3	-7
1302n3	41664eb4	31248cb4	72912dc4

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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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