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	97344dk	Isogeny class
Conductor	97344	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-6.6406035920337E+22	Discriminant
Eigenvalues	2+ 3-  3  3  0 13-  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31346796,-68680293968]	[a1,a2,a3,a4,a6]
Generators	[2516051799012433685973935164313173031318996138372520:-468830579238071489378688295436368549791142921187804492:70568068638044730105149219529468815377228531375]	Generators of the group modulo torsion
j	-1680914269/32768	j-invariant
L	9.934786966266	L(r)(E,1)/r!
Ω	0.031865405684228	Real period
R	77.943358580738	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	97344gn2 3042o2 10816t2 97344dn2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344dk2

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
+	-	3	3	0	-	3	-6	-6	0	0	-3	0	-1	-3	-6	-6	8	-12	15	6	10	-6	6	12

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Quadratic twists for elliptic curve 97344dk2

-4	8	-3	13
97344gn2	3042o2	10816t2	97344dn2

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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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