Cremona's table of elliptic curves

97498 = 2 · 29 · 41²

Field	Data	Notes
Atkin-Lehner	2- 29- 41+	Signs for the Atkin-Lehner involutions
Class	97498k	Isogeny class
Conductor	97498	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	-389720383410731636 = -1 · 22 · 295 · 416	Discriminant
Eigenvalues	2-  1  1  2  3  1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-764890,-259291496]	[a1,a2,a3,a4,a6]
Generators	[6632340:254323976:3375]	Generators of the group modulo torsion
j	-10418796526321/82044596	j-invariant
L	14.793913008201	L(r)(E,1)/r!
Ω	0.080679951774553	Real period
R	9.1682708623782	Regulator
r	1	Rank of the group of rational points
S	0.99999999915819	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58b2	Quadratic twists by: 41

Hecke Eigenvalues for elliptic curve 97498k2

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	2	3	1	-8	0	4	-	-3	8	+	-11	-13	11	0	-8	12	-2	4	-15	4	10	2

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Quadratic twists for elliptic curve 97498k2

41
58b2

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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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