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	31920k	Isogeny class
Conductor	31920	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	153222465715200 = 210 · 38 · 52 · 7 · 194	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13480,95200]	[a1,a2,a3,a4,a6]
Generators	[205:2430:1]	Generators of the group modulo torsion
j	264560893944484/149631314175	j-invariant
L	5.0186279206861	L(r)(E,1)/r!
Ω	0.49720479795365	Real period
R	2.5234209028861	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15960i3 127680fo4 95760z4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31920k4

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	+	-8	6	8	-10	6	-4	-8	-2	4	6	8	4	2	-4	-12	6	-18

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Quadratic twists for elliptic curve 31920k4

-4	8	-3
15960i3	127680fo4	95760z4

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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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