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	31740a	Isogeny class
Conductor	31740	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	662400	Modular degree for the optimal curve
Δ	-3044731107725280000 = -1 · 28 · 35 · 54 · 238	Discriminant
Eigenvalues	2- 3+ 5+  3 -6 -3  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129781,85902625]	[a1,a2,a3,a4,a6]
Generators	[8288:753825:1]	Generators of the group modulo torsion
j	-12058624/151875	j-invariant
L	4.2039022921385	L(r)(E,1)/r!
Ω	0.21479818938299	Real period
R	3.2619007824772	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	126960cr1 95220bd1 31740c1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 31740a1

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
-	+	+	3	-6	-3	2	0	-	6	8	-5	12	-5	-4	-6	8	-9	-7	4	-14	16	-14	-12	-6

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Quadratic twists for elliptic curve 31740a1

-4	-3	-23
126960cr1	95220bd1	31740c1

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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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