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	34848r	Isogeny class
Conductor	34848	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	-58188380811264 = -1 · 212 · 36 · 117	Discriminant
Eigenvalues	2+ 3- -1  4 11-  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-49368,4237904]	[a1,a2,a3,a4,a6]
Generators	[440:8228:1]	Generators of the group modulo torsion
j	-2515456/11	j-invariant
L	6.5464457050273	L(r)(E,1)/r!
Ω	0.62903735951418	Real period
R	2.6017714234345	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34848s1 69696fx1 3872j1 3168x1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 34848r1

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	4	-	2	0	-2	9	4	-5	-9	2	-6	-4	6	-5	0	13	-1	-14	-10	-14	13	-19

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Quadratic twists for elliptic curve 34848r1

-4	8	-3	-11
34848s1	69696fx1	3872j1	3168x1

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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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