Cremona's table of elliptic curves

97344 = 2⁶ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13-	Signs for the Atkin-Lehner involutions
Class	97344dd	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4559740625633476608 = 216 · 38 · 139	Discriminant
Eigenvalues	2+ 3-  2 -2 -4 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1608204,778230128]	[a1,a2,a3,a4,a6]
Generators	[6301:490725:1]	Generators of the group modulo torsion
j	907924/9	j-invariant
L	6.9806050984476	L(r)(E,1)/r!
Ω	0.24582764692472	Real period
R	7.0990846489911	Regulator
r	1	Rank of the group of rational points
S	1.0000000000178	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344gh2 12168w2 32448s2 97344df2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344dd2

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
+	-	2	-2	-4	-	6	2	-4	6	-2	-8	6	-4	8	2	-8	14	14	12	4	0	0	-6	-12

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Quadratic twists for elliptic curve 97344dd2

-4	8	-3	13
97344gh2	12168w2	32448s2	97344df2

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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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