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	10416v	Isogeny class
Conductor	10416	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-14335082496 = -1 · 220 · 32 · 72 · 31	Discriminant
Eigenvalues	2- 3+ -2 7+  6  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-504,-7056]	[a1,a2,a3,a4,a6]
Generators	[42:210:1]	Generators of the group modulo torsion
j	-3463512697/3499776	j-invariant
L	3.5122637964071	L(r)(E,1)/r!
Ω	0.48404637837357	Real period
R	1.8140120210219	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	1302g1 41664dp1 31248bs1 72912ck1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416v1

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	+	6	4	0	4	-6	-10	-	-2	-10	-2	0	10	12	-12	8	-12	-12	14	0	0	14

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Quadratic twists for elliptic curve 10416v1

-4	8	-3	-7
1302g1	41664dp1	31248bs1	72912ck1

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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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