Cremona's table of elliptic curves

5200 = 2⁴ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	5200ba	Isogeny class
Conductor	5200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	665600000000000 = 220 · 511 · 13	Discriminant
Eigenvalues	2-  2 5+ -4  2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-336408,75203312]	[a1,a2,a3,a4,a6]
Generators	[-478:11250:1]	Generators of the group modulo torsion
j	65787589563409/10400000	j-invariant
L	4.8271812932169	L(r)(E,1)/r!
Ω	0.49408240234144	Real period
R	2.4424980885481	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	650e1 20800cr1 46800el1 1040e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200ba1

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	+	-4	2	-	-2	-6	6	2	6	2	10	-10	-12	-2	-10	2	-12	-10	-10	4	0	-14	-14

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Quadratic twists for elliptic curve 5200ba1

-4	8	-3	5	13
650e1	20800cr1	46800el1	1040e1	67600by1

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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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