Cremona's table of elliptic curves

497 = 7 · 71

Field	Data	Notes
Atkin-Lehner	7- 71-	Signs for the Atkin-Lehner involutions
Class	497a	Isogeny class
Conductor	497	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-1193297 = -1 · 75 · 71	Discriminant
Eigenvalues	1 -1  0 7-  1 -3 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,25,-14]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	1622234375/1193297	j-invariant
L	2.0670876477823	L(r)(E,1)/r!
Ω	1.5344348415755	Real period
R	0.26942657866918	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	7952b1 31808m1 4473a1 12425c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 497a1

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	-1	0	-	1	-3	-2	-4	-9	-1	4	-3	9	0	0	2	-8	5	0	-	-4	-10	9	8	5

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Quadratic twists for elliptic curve 497a1

-4	8	-3	5	-7	-11	13	-71
7952b1	31808m1	4473a1	12425c1	3479f1	60137a1	83993a1	35287a1

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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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