Cremona's table of elliptic curves

31827 = 3 · 103²

Field	Data	Notes
Atkin-Lehner	3- 103+	Signs for the Atkin-Lehner involutions
Class	31827c	Isogeny class
Conductor	31827	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-38003102441628483 = -1 · 3 · 1038	Discriminant
Eigenvalues	2 3- -4  1 -2  1  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-43888651470,-3538981270115995]	[a1,a2,a3,a4,a6]
j	-738044630625096380416/3	j-invariant
L	2.6441705211402	L(r)(E,1)/r!
Ω	0.0052153264716789	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	169	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	95481c2 31827b2	Quadratic twists by: -3 -103

Hecke Eigenvalues for elliptic curve 31827c2

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	-	-4	1	-2	1	0	1	-2	-8	-7	-1	2	-5	10	-14	4	10	8	-8	9	15	-2	12	14

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Quadratic twists for elliptic curve 31827c2

-3	-103
95481c2	31827b2

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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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