Cremona's table of elliptic curves

6292 = 2² · 11² · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	6292f	Isogeny class
Conductor	6292	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	19008	Modular degree for the optimal curve
Δ	5394984317008 = 24 · 1110 · 13	Discriminant
Eigenvalues	2- -1  4  0 11- 13+ -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-19521,-1037342]	[a1,a2,a3,a4,a6]
Generators	[-83:65:1]	Generators of the group modulo torsion
j	1982464/13	j-invariant
L	4.1644296217144	L(r)(E,1)/r!
Ω	0.4040580579834	Real period
R	3.4355043286754	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	25168w1 100672bl1 56628s1 6292j1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6292f1

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
-	-1	4	0	-	+	-3	-6	7	-9	-8	2	8	7	2	-9	4	-7	8	-14	-14	5	2	0	-4

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Quadratic twists for elliptic curve 6292f1

-4	8	-3	-11	13
25168w1	100672bl1	56628s1	6292j1	81796k1

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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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