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	5712b	Isogeny class
Conductor	5712	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3385525248 = -1 · 210 · 34 · 74 · 17	Discriminant
Eigenvalues	2+ 3+ -2 7+  4  6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,216,-2592]	[a1,a2,a3,a4,a6]
j	1083360092/3306177	j-invariant
L	1.444474580669	L(r)(E,1)/r!
Ω	0.72223729033451	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2856c4 22848co3 17136d4 39984p3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712b4

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

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Quadratic twists for elliptic curve 5712b4

-4	8	-3	-7	17
2856c4	22848co3	17136d4	39984p3	97104bb3

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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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