Cremona's table of elliptic curves

82418 = 2 · 7² · 29²

Field	Data	Notes
Atkin-Lehner	2+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	82418i	Isogeny class
Conductor	82418	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1096200	Modular degree for the optimal curve
Δ	117706980476897378 = 2 · 76 · 298	Discriminant
Eigenvalues	2+  2  0 7- -6  4  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-124485,-3702061]	[a1,a2,a3,a4,a6]
Generators	[-1442412:16758235:46656]	Generators of the group modulo torsion
j	3625/2	j-invariant
L	6.9641882707529	L(r)(E,1)/r!
Ω	0.2720237455357	Real period
R	8.5337994429873	Regulator
r	1	Rank of the group of rational points
S	1.0000000009129	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1682d1 82418q1	Quadratic twists by: -7 29

Hecke Eigenvalues for elliptic curve 82418i1

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	-	-6	4	3	4	9	-	-5	2	6	-4	9	-12	-6	-2	8	3	-11	11	0	-3	-17

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Quadratic twists for elliptic curve 82418i1

-7	29
1682d1	82418q1

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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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