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	4550b	Isogeny class
Conductor	4550	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-2843750 = -1 · 2 · 56 · 7 · 13	Discriminant
Eigenvalues	2+ -1 5+ 7+ -3 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-391575,-94476125]	[a1,a2,a3,a4,a6]
Generators	[181215:77051255:1]	Generators of the group modulo torsion
j	-424962187484640625/182	j-invariant
L	2.0039403256985	L(r)(E,1)/r!
Ω	0.095425770538235	Real period
R	10.499995516911	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36400bq3 40950dr3 182b3 31850v3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550b3

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
+	-1	+	+	-3	+	0	2	3	0	5	7	3	-8	3	12	6	-1	-5	12	-11	-1	-12	-18	-17

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Quadratic twists for elliptic curve 4550b3

-4	-3	5	-7	13
36400bq3	40950dr3	182b3	31850v3	59150bv3

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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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