Cremona's table of elliptic curves

31680 = 2⁶ · 3² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11-	Signs for the Atkin-Lehner involutions
Class	31680ee	Isogeny class
Conductor	31680	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	397434470400 = 214 · 36 · 52 · 113	Discriminant
Eigenvalues	2- 3- 5-  4 11-  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-255612,-49741616]	[a1,a2,a3,a4,a6]
Generators	[4208:270900:1]	Generators of the group modulo torsion
j	154639330142416/33275	j-invariant
L	7.408494640889	L(r)(E,1)/r!
Ω	0.21232652434695	Real period
R	5.8153314128441	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	31680bo4 7920ba4 3520u4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31680ee4

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	-	4	0	-4	-6	-6	-8	-2	-6	8	6	-6	12	-2	-10	-12	-16	-8	0	-6	14

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Quadratic twists for elliptic curve 31680ee4

-4	8	-3
31680bo4	7920ba4	3520u4

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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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