Cremona's table of elliptic curves

5194 = 2 · 7² · 53

Field	Data	Notes
Atkin-Lehner	2+ 7- 53+	Signs for the Atkin-Lehner involutions
Class	5194g	Isogeny class
Conductor	5194	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	41552 = 24 · 72 · 53	Discriminant
Eigenvalues	2+  2  0 7- -3  1  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-620,-6208]	[a1,a2,a3,a4,a6]
j	539258169625/848	j-invariant
L	1.9131124569201	L(r)(E,1)/r!
Ω	0.95655622846003	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41552bl1 46746bo1 129850cv1 5194b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5194g1

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	-	-3	1	3	-2	0	3	-8	11	6	11	9	+	3	10	8	6	-2	-4	12	-9	-2

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Quadratic twists for elliptic curve 5194g1

-4	-3	5	-7
41552bl1	46746bo1	129850cv1	5194b1

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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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