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	31920bg	Isogeny class
Conductor	31920	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	63360	Modular degree for the optimal curve
Δ	-3687398400000 = -1 · 213 · 3 · 55 · 7 · 193	Discriminant
Eigenvalues	2- 3+ 5- 7-  1  1 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2480,78400]	[a1,a2,a3,a4,a6]
Generators	[240:3800:1]	Generators of the group modulo torsion
j	411664745519/900243750	j-invariant
L	5.1252172661546	L(r)(E,1)/r!
Ω	0.54669556059773	Real period
R	0.15624836549953	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3990z1 127680ff1 95760dt1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31920bg1

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	-4	-	-7	-8	-9	12	6	-5	-12	11	9	5	0	-1	1	8	15	16	-10

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Quadratic twists for elliptic curve 31920bg1

-4	8	-3
3990z1	127680ff1	95760dt1

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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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