Cremona's table of elliptic curves

31200 = 2⁵ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	31200bu	Isogeny class
Conductor	31200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	38025000000 = 26 · 32 · 58 · 132	Discriminant
Eigenvalues	2- 3- 5+  0  4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1158,-12312]	[a1,a2,a3,a4,a6]
Generators	[6154:170625:8]	Generators of the group modulo torsion
j	171879616/38025	j-invariant
L	7.2483057709106	L(r)(E,1)/r!
Ω	0.83127004927107	Real period
R	4.3597780151387	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31200be1 62400eq2 93600w1 6240c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200bu1

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

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Quadratic twists for elliptic curve 31200bu1

-4	8	-3	5
31200be1	62400eq2	93600w1	6240c1

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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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