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	31600o	Isogeny class
Conductor	31600	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	5301600256000000 = 232 · 56 · 79	Discriminant
Eigenvalues	2- -1 5+  3 -2  1  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-168008,-26217488]	[a1,a2,a3,a4,a6]
Generators	[-782490:1577402:3375]	Generators of the group modulo torsion
j	8194759433281/82837504	j-invariant
L	4.6231842273933	L(r)(E,1)/r!
Ω	0.23595650626119	Real period
R	9.7966873231198	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	3950a1 126400by1 1264e1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 31600o1

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	+	3	-2	1	2	0	-6	-10	-2	2	2	4	3	-4	-5	12	8	13	6	-	-6	-15	-13

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Quadratic twists for elliptic curve 31600o1

-4	8	5
3950a1	126400by1	1264e1

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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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