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	34848cg	Isogeny class
Conductor	34848	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	40960	Modular degree for the optimal curve
Δ	743885550144 = 26 · 38 · 116	Discriminant
Eigenvalues	2- 3- -2 -4 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2541,-26620]	[a1,a2,a3,a4,a6]
Generators	[-43:56:1] [-17:108:1]	Generators of the group modulo torsion
j	21952/9	j-invariant
L	7.1310630138578	L(r)(E,1)/r!
Ω	0.69706081528028	Real period
R	5.1150938752666	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	34848ba1 69696co2 11616e1 288c1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 34848cg1

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	-	2	-6	-4	0	2	-4	-2	2	4	8	-10	-4	-6	-4	-16	6	4	-12	-10	-14

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Quadratic twists for elliptic curve 34848cg1

-4	8	-3	-11
34848ba1	69696co2	11616e1	288c1

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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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