Cremona's table of elliptic curves

31600 = 2⁴ · 5² · 79

Field	Data	Notes
Atkin-Lehner	2- 5+ 79+	Signs for the Atkin-Lehner involutions
Class	31600g	Isogeny class
Conductor	31600	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1325400064000000 = 230 · 56 · 79	Discriminant
Eigenvalues	2-  1 5+ -1  0 -5  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2086608,1159440788]	[a1,a2,a3,a4,a6]
j	15698803397448457/20709376	j-invariant
L	0.81752947702088	L(r)(E,1)/r!
Ω	0.40876473851007	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3950h3 126400bl3 1264b3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 31600g3

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
-	1	+	-1	0	-5	0	-2	-6	0	4	-2	-12	8	-9	-6	9	8	-4	9	-2	+	18	9	-17

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Quadratic twists for elliptic curve 31600g3

-4	8	5
3950h3	126400bl3	1264b3

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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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