Cremona's table of elliptic curves

5712 = 2⁴ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	5712j	Isogeny class
Conductor	5712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3592071168 = 211 · 3 · 7 · 174	Discriminant
Eigenvalues	2+ 3-  2 7+  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-992,-12012]	[a1,a2,a3,a4,a6]
j	52767497666/1753941	j-invariant
L	3.4094168686338	L(r)(E,1)/r!
Ω	0.85235421715845	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2856f4 22848bu3 17136g4 39984i3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712j3

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

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Quadratic twists for elliptic curve 5712j3

-4	8	-3	-7	17
2856f4	22848bu3	17136g4	39984i3	97104h3

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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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