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	10416ba	Isogeny class
Conductor	10416	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2231857152 = 212 · 34 · 7 · 312	Discriminant
Eigenvalues	2- 3+ -2 7-  2 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-504,3888]	[a1,a2,a3,a4,a6]
Generators	[-22:62:1]	Generators of the group modulo torsion
j	3463512697/544887	j-invariant
L	3.3044354518361	L(r)(E,1)/r!
Ω	1.3978061606376	Real period
R	1.1820077579028	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	651c2 41664ea2 31248bz2 72912da2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416ba2

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	-	2	-4	0	4	-2	-2	+	-2	6	2	8	2	4	-4	0	-12	4	2	-8	0	-2

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Quadratic twists for elliptic curve 10416ba2

-4	8	-3	-7
651c2	41664ea2	31248bz2	72912da2

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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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