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	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	299008 = 212 · 73	Discriminant
Eigenvalues	2-  0  0 -4  2  0  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-100,-384]	[a1,a2,a3,a4,a6]
Generators	[12:12:1]	Generators of the group modulo torsion
j	27000000/73	j-invariant
L	3.2983827343556	L(r)(E,1)/r!
Ω	1.5099762893983	Real period
R	2.1843937269174	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	4672b1 2336b1 42048cb1 116800bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4672c1

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 4672c1

-4	8	-3	5
4672b1	2336b1	42048cb1	116800bp1

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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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