Cremona's table of elliptic curves

5300 = 2² · 5² · 53

Field	Data	Notes
Atkin-Lehner	2- 5- 53-	Signs for the Atkin-Lehner involutions
Class	5300g	Isogeny class
Conductor	5300	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	3312	Modular degree for the optimal curve
Δ	8480000 = 28 · 54 · 53	Discriminant
Eigenvalues	2- -2 5- -5  1  2 -7 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-933,10663]	[a1,a2,a3,a4,a6]
Generators	[57:-382:1] [-7:130:1]	Generators of the group modulo torsion
j	561971200/53	j-invariant
L	3.4789158536103	L(r)(E,1)/r!
Ω	2.2238227654185	Real period
R	0.17382059936064	Regulator
r	2	Rank of the group of rational points
S	0.99999999999959	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21200z1 84800bf1 47700l1 5300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5300g1

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	-	-5	1	2	-7	-8	-8	2	-8	-5	2	-1	-8	-	3	0	-8	-4	-10	-10	6	-15	-14

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Quadratic twists for elliptic curve 5300g1

-4	8	-3	5
21200z1	84800bf1	47700l1	5300c1

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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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