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	5712r	Isogeny class
Conductor	5712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-501559296 = -1 · 212 · 3 · 74 · 17	Discriminant
Eigenvalues	2- 3-  1 7+  5 -5 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-85,1091]	[a1,a2,a3,a4,a6]
j	-16777216/122451	j-invariant
L	2.8419363427747	L(r)(E,1)/r!
Ω	1.4209681713873	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	357b1 22848bv1 17136w1 39984bp1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712r1

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
-	-	1	+	5	-5	-	5	1	-6	6	4	7	7	-6	6	-14	0	12	-4	6	6	6	12	8

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Quadratic twists for elliptic curve 5712r1

-4	8	-3	-7	17
357b1	22848bv1	17136w1	39984bp1	97104bz1

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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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