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	34848bn	Isogeny class
Conductor	34848	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	92160	Modular degree for the optimal curve
Δ	24548223154752 = 26 · 39 · 117	Discriminant
Eigenvalues	2- 3+ -2 -4 11- -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9801,-287496]	[a1,a2,a3,a4,a6]
Generators	[-44:242:1]	Generators of the group modulo torsion
j	46656/11	j-invariant
L	2.7930383042936	L(r)(E,1)/r!
Ω	0.4880072220017	Real period
R	1.430838611792	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34848bm1 69696eo1 34848f1 3168f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 34848bn1

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	-4	-	-4	-6	2	-6	2	8	6	-2	-6	2	-6	-8	12	-4	14	10	-8	4	8	-10

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Quadratic twists for elliptic curve 34848bn1

-4	8	-3	-11
34848bm1	69696eo1	34848f1	3168f1

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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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