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	5200b	Isogeny class
Conductor	5200	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-67600000000 = -1 · 210 · 58 · 132	Discriminant
Eigenvalues	2+  2 5+  0 -2 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,12512]	[a1,a2,a3,a4,a6]
Generators	[22:150:1]	Generators of the group modulo torsion
j	-4/4225	j-invariant
L	5.1453434462321	L(r)(E,1)/r!
Ω	0.87446339529278	Real period
R	1.4710002368108	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	2600a2 20800dg2 46800m2 1040b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200b2

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	+	0	-2	+	-2	-2	2	-6	-2	6	2	6	-8	2	-6	-14	0	-10	2	4	12	-6	-2

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Quadratic twists for elliptic curve 5200b2

-4	8	-3	5	13
2600a2	20800dg2	46800m2	1040b2	67600m2

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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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