Cremona's table of elliptic curves

5203 = 11² · 43

Field	Data	Notes
Atkin-Lehner	11- 43-	Signs for the Atkin-Lehner involutions
Class	5203a	Isogeny class
Conductor	5203	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24480	Modular degree for the optimal curve
Δ	-4359845280659 = -1 · 119 · 432	Discriminant
Eigenvalues	2  1 -1  0 11-  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-121766,-16395461]	[a1,a2,a3,a4,a6]
Generators	[12310102:822036207:2744]	Generators of the group modulo torsion
j	-112706583998464/2461019	j-invariant
L	7.8246187135742	L(r)(E,1)/r!
Ω	0.12778714958198	Real period
R	7.6539569306954	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	83248ba1 46827u1 473a1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 5203a1

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	1	-1	0	-	2	-6	8	-1	-6	-1	-3	4	-	-8	-14	9	4	9	-13	16	-16	6	-7	13

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Quadratic twists for elliptic curve 5203a1

-4	-3	-11
83248ba1	46827u1	473a1

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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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