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	5712o	Isogeny class
Conductor	5712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-2958176256 = -1 · 212 · 3 · 72 · 173	Discriminant
Eigenvalues	2- 3+  1 7- -1  1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,315,1389]	[a1,a2,a3,a4,a6]
Generators	[-4:7:1]	Generators of the group modulo torsion
j	841232384/722211	j-invariant
L	3.6893458031571	L(r)(E,1)/r!
Ω	0.926318122868	Real period
R	1.9914032296672	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	357c1 22848cr1 17136bn1 39984dp1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712o1

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	-	-1	1	+	-1	3	-2	0	-6	-1	-5	-12	0	0	-2	8	0	6	4	-6	16	-12

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Quadratic twists for elliptic curve 5712o1

-4	8	-3	-7	17
357c1	22848cr1	17136bn1	39984dp1	97104ch1

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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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