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	4550c	Isogeny class
Conductor	4550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3233584935546875000 = 23 · 512 · 73 · 136	Discriminant
Eigenvalues	2+  2 5+ 7+  0 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-508900,109515000]	[a1,a2,a3,a4,a6]
Generators	[409305:50137535:27]	Generators of the group modulo torsion
j	932829715460155969/206949435875000	j-invariant
L	3.7107942594063	L(r)(E,1)/r!
Ω	0.23750721704001	Real period
R	7.8119610546008	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	36400bx4 40950dl4 910j4 31850bc4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550c4

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	+	+	0	+	0	2	-6	6	-4	-2	0	-8	0	-12	6	-10	4	6	-2	8	-12	0	10

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Quadratic twists for elliptic curve 4550c4

-4	-3	5	-7	13
36400bx4	40950dl4	910j4	31850bc4	59150bx4

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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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