Cremona's table of elliptic curves

31920 = 2⁴ · 3 · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7- 19+	Signs for the Atkin-Lehner involutions
Class	31920bx	Isogeny class
Conductor	31920	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	-6308998214400000000 = -1 · 214 · 32 · 58 · 78 · 19	Discriminant
Eigenvalues	2- 3- 5- 7- -4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-441840,165330900]	[a1,a2,a3,a4,a6]
Generators	[-462:16464:1]	Generators of the group modulo torsion
j	-2328948245994395761/1540282767187500	j-invariant
L	7.2798343013208	L(r)(E,1)/r!
Ω	0.21990128244717	Real period
R	1.0345315833751	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3990u6 127680ee5 95760dm5	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31920bx5

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
-	-	-	-	-4	-2	2	+	0	6	0	-2	-6	-12	8	-10	4	14	-4	0	10	-8	-12	10	-14

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Quadratic twists for elliptic curve 31920bx5

-4	8	-3
3990u6	127680ee5	95760dm5

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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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