Cremona's table of elliptic curves

4672 = 2⁶ · 73

Field	Data	Notes
Atkin-Lehner	2- 73-	Signs for the Atkin-Lehner involutions
Class	4672d	Isogeny class
Conductor	4672	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	19136512 = 218 · 73	Discriminant
Eigenvalues	2-  0 -2 -2 -2  6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-76,144]	[a1,a2,a3,a4,a6]
Generators	[0:12:1]	Generators of the group modulo torsion
j	185193/73	j-invariant
L	3.0111403432401	L(r)(E,1)/r!
Ω	1.9747967190009	Real period
R	1.5247849635701	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4672a1 1168a1 42048cg1 116800bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4672d1

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

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Quadratic twists for elliptic curve 4672d1

-4	8	-3	5
4672a1	1168a1	42048cg1	116800bk1

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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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