Cremona's table of elliptic curves

48032 = 2⁵ · 19 · 79

Field	Data	Notes
Atkin-Lehner	2- 19- 79-	Signs for the Atkin-Lehner involutions
Class	48032f	Isogeny class
Conductor	48032	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	294912	Modular degree for the optimal curve
Δ	263181662285824 = 212 · 194 · 793	Discriminant
Eigenvalues	2- -3 -3  1 -2 -1 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23164,1110016]	[a1,a2,a3,a4,a6]
Generators	[122:316:1] [-115:1501:1]	Generators of the group modulo torsion
j	335586462343488/64253335519	j-invariant
L	4.7976574190991	L(r)(E,1)/r!
Ω	0.52404821632284	Real period
R	0.19072900759501	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48032b1 96064y1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 48032f1

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
-	-3	-3	1	-2	-1	-6	-	-6	6	-2	2	-6	4	-7	12	-1	-8	8	-11	10	-	-18	5	-15

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Quadratic twists for elliptic curve 48032f1

-4	8
48032b1	96064y1

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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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