Cremona's table of elliptic curves

4672 = 2⁶ · 73

Field	Data	Notes
Atkin-Lehner	2- 73-	Signs for the Atkin-Lehner involutions
Class	4672c	Isogeny class
Conductor	4672	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	174620672 = 215 · 732	Discriminant
Eigenvalues	2-  0  0 -4  2  0  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-140,-48]	[a1,a2,a3,a4,a6]
Generators	[-6:24:1]	Generators of the group modulo torsion
j	9261000/5329	j-invariant
L	3.2983827343556	L(r)(E,1)/r!
Ω	1.5099762893983	Real period
R	1.0921968634587	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	4672b2 2336b2 42048cb2 116800bp2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4672c2

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

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Quadratic twists for elliptic curve 4672c2

-4	8	-3	5
4672b2	2336b2	42048cb2	116800bp2

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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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