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	31680dc	Isogeny class
Conductor	31680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1231718400000000 = 217 · 37 · 58 · 11	Discriminant
Eigenvalues	2- 3- 5+ -4 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-58188,-5131888]	[a1,a2,a3,a4,a6]
Generators	[-148:488:1] [-128:468:1]	Generators of the group modulo torsion
j	228027144098/12890625	j-invariant
L	7.4237344294078	L(r)(E,1)/r!
Ω	0.30847502526474	Real period
R	12.032958621265	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31680p4 7920p3 10560bw3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31680dc4

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

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Quadratic twists for elliptic curve 31680dc4

-4	8	-3
31680p4	7920p3	10560bw3

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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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