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	34848t	Isogeny class
Conductor	34848	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	810091364106816 = 26 · 310 · 118	Discriminant
Eigenvalues	2+ 3-  2  0 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-37389,-2422420]	[a1,a2,a3,a4,a6]
Generators	[5548244:105615900:12167]	Generators of the group modulo torsion
j	69934528/9801	j-invariant
L	7.2147951088094	L(r)(E,1)/r!
Ω	0.34653005999865	Real period
R	10.410056646799	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	34848bz1 69696cq2 11616t1 3168u1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 34848t1

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

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Quadratic twists for elliptic curve 34848t1

-4	8	-3	-11
34848bz1	69696cq2	11616t1	3168u1

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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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