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	6292d	Isogeny class
Conductor	6292	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-102014248903424 = -1 · 28 · 119 · 132	Discriminant
Eigenvalues	2-  1  3 -2 11- 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10971,204983]	[a1,a2,a3,a4,a6]
Generators	[-14:221:1]	Generators of the group modulo torsion
j	321978368/224939	j-invariant
L	5.1738861309089	L(r)(E,1)/r!
Ω	0.37792303303356	Real period
R	3.4225792546821	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	25168ba1 100672bt1 56628q1 572a1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6292d1

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	3	-2	-	+	0	-2	-3	6	-1	-7	-6	-8	12	-6	9	-2	-7	-3	-8	4	12	-15	-13

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Quadratic twists for elliptic curve 6292d1

-4	8	-3	-11	13
25168ba1	100672bt1	56628q1	572a1	81796g1

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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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