Cremona's table of elliptic curves

4550 = 2 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	4550w	Isogeny class
Conductor	4550	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	1274000 = 24 · 53 · 72 · 13	Discriminant
Eigenvalues	2- -2 5- 7+  2 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-48,112]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	97972181/10192	j-invariant
L	3.8599792442003	L(r)(E,1)/r!
Ω	2.6407496040098	Real period
R	0.36542457853059	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	36400cs1 40950bv1 4550m1 31850cp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550w1

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
-	-2	-	+	2	+	2	0	-8	-2	4	2	0	-8	-4	4	4	2	-12	-2	10	0	-4	4	-14

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Quadratic twists for elliptic curve 4550w1

-4	-3	5	-7	13
36400cs1	40950bv1	4550m1	31850cp1	59150ba1

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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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