Cremona's table of elliptic curves

53 = Prime conductor

Field	Data	Notes
Atkin-Lehner	53+	Signs for the Atkin-Lehner involutions
Class	53a	Isogeny class
Conductor	53	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-53 = Prime discriminant	Discriminant
Eigenvalues	-1 -3  0 -4  0 -3 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,0,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	3375/53	j-invariant
L	0.43586382417786	L(r)(E,1)/r!
Ω	4.6876410488789	Real period
R	0.092981484638654	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	848e1 3392k1 477a1 1325c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 53a1

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	-4	0	-3	-3	-5	7	-7	4	5	6	-2	-2	+	-2	-8	-12	1	-4	-1	-1	-14	1

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Quadratic twists for elliptic curve 53a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
848e1	3392k1	477a1	1325c1	2597d1	6413g1	8957b1	15317g1	19133a1	28037c1	44573a1	50933a1	72557a1	89093d1	97997a1	117077a1	2809a1

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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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