Cremona's table of elliptic curves

31824 = 2⁴ · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	31824r	Isogeny class
Conductor	31824	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	73603541127168 = 212 · 314 · 13 · 172	Discriminant
Eigenvalues	2- 3-  0  2 -2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14115,496226]	[a1,a2,a3,a4,a6]
Generators	[145:-1224:1]	Generators of the group modulo torsion
j	104154702625/24649677	j-invariant
L	5.6096557866298	L(r)(E,1)/r!
Ω	0.57702483874126	Real period
R	1.2152110728169	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1989a2 127296cn2 10608o2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31824r2

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

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Quadratic twists for elliptic curve 31824r2

-4	8	-3
1989a2	127296cn2	10608o2

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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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