Cremona's table of elliptic curves

6834 = 2 · 3 · 17 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 67-	Signs for the Atkin-Lehner involutions
Class	6834w	Isogeny class
Conductor	6834	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	550851043656 = 23 · 3 · 17 · 675	Discriminant
Eigenvalues	2- 3-  3 -5  1 -7 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2584,35576]	[a1,a2,a3,a4,a6]
Generators	[-50:226:1]	Generators of the group modulo torsion
j	1908146629143937/550851043656	j-invariant
L	7.2619466200693	L(r)(E,1)/r!
Ω	0.85824298763598	Real period
R	0.56409406385576	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54672u1 20502o1 116178w1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 6834w1

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
-	-	3	-5	1	-7	-	-6	0	0	3	-2	-10	-8	0	6	-3	-10	-	5	-10	7	4	-16	1

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Quadratic twists for elliptic curve 6834w1

-4	-3	17
54672u1	20502o1	116178w1

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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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