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	5194j	Isogeny class
Conductor	5194	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2987241663040294688 = 25 · 716 · 532	Discriminant
Eigenvalues	2+ -2  4 7-  0  4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-23473574,-43775947176]	[a1,a2,a3,a4,a6]
Generators	[547187324700:75154138307707:27000000]	Generators of the group modulo torsion
j	12158306898176952482761/25391135182112	j-invariant
L	2.6706418317841	L(r)(E,1)/r!
Ω	0.068589052997055	Real period
R	19.468426192579	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	41552bt2 46746bk2 129850ce2 742e2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5194j2

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	-	0	4	2	-6	-8	-6	8	-6	-2	-8	-4	-	-2	-12	-4	-8	2	8	-6	-2	2

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Quadratic twists for elliptic curve 5194j2

-4	-3	5	-7
41552bt2	46746bk2	129850ce2	742e2

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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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