Cremona's table of elliptic curves

31740 = 2² · 3 · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23-	Signs for the Atkin-Lehner involutions
Class	31740k	Isogeny class
Conductor	31740	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	2380500000000 = 28 · 32 · 59 · 232	Discriminant
Eigenvalues	2- 3- 5- -2  3 -4  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17725,899375]	[a1,a2,a3,a4,a6]
Generators	[50:-375:1]	Generators of the group modulo torsion
j	4547904200704/17578125	j-invariant
L	7.1473771643108	L(r)(E,1)/r!
Ω	0.8207527831475	Real period
R	0.48379550734586	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	126960bw2 95220q2 31740e2	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 31740k2

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
-	-	-	-2	3	-4	0	7	-	-6	5	-2	-9	-2	6	-6	0	-5	-2	-9	2	1	-6	-6	10

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Quadratic twists for elliptic curve 31740k2

-4	-3	-23
126960bw2	95220q2	31740e2

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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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