Cremona's table of elliptic curves

4650 = 2 · 3 · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 31+	Signs for the Atkin-Lehner involutions
Class	4650bi	Isogeny class
Conductor	4650	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	267840000000 = 212 · 33 · 57 · 31	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2713,-48583]	[a1,a2,a3,a4,a6]
Generators	[-28:89:1]	Generators of the group modulo torsion
j	141339344329/17141760	j-invariant
L	6.110075786926	L(r)(E,1)/r!
Ω	0.66676333050773	Real period
R	0.25454958251134	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	37200bv1 13950m1 930a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 4650bi1

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	-4	-6	-2	-4	4	2	+	2	-6	4	0	-2	-4	-6	-16	-12	6	-16	12	-18	14

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Quadratic twists for elliptic curve 4650bi1

-4	-3	5
37200bv1	13950m1	930a1

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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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