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	6834n	Isogeny class
Conductor	6834	Conductor
∏ cp	400	Product of Tamagawa factors cp
deg	172800	Modular degree for the optimal curve
Δ	541351250664357888 = 220 · 34 · 175 · 672	Discriminant
Eigenvalues	2- 3+  0  0  4 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2418878,-1448576773]	[a1,a2,a3,a4,a6]
Generators	[-903:1063:1]	Generators of the group modulo torsion
j	1565184783388747048998625/541351250664357888	j-invariant
L	5.2527568539711	L(r)(E,1)/r!
Ω	0.12106122862223	Real period
R	0.43389257764451	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	54672bj1 20502f1 116178bb1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 6834n1

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
-	+	0	0	4	-6	-	0	-6	6	-4	-2	0	4	4	10	-12	-8	+	-6	-2	-12	-4	-10	-16

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Quadratic twists for elliptic curve 6834n1

-4	-3	17
54672bj1	20502f1	116178bb1

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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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