Cremona's table of elliptic curves

34848 = 2⁵ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	34848u	Isogeny class
Conductor	34848	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	17281949100945408 = 212 · 39 · 118	Discriminant
Eigenvalues	2+ 3-  2  2 11-  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-140844,19336768]	[a1,a2,a3,a4,a6]
Generators	[-66:5324:1]	Generators of the group modulo torsion
j	58411072/3267	j-invariant
L	7.4680288580074	L(r)(E,1)/r!
Ω	0.38368244500754	Real period
R	1.2165054974466	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34848v2 69696gn1 11616bc2 3168v2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 34848u2

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	-	2	0	2	0	-8	-4	-6	-4	6	-8	6	-4	6	-4	-8	10	-14	8	-2	14

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Quadratic twists for elliptic curve 34848u2

-4	8	-3	-11
34848v2	69696gn1	11616bc2	3168v2

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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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