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	31200be	Isogeny class
Conductor	31200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	42120000000 = 29 · 34 · 57 · 13	Discriminant
Eigenvalues	2- 3+ 5+  0 -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17408,889812]	[a1,a2,a3,a4,a6]
Generators	[-148:450:1] [52:350:1]	Generators of the group modulo torsion
j	72929847752/5265	j-invariant
L	7.1705730217675	L(r)(E,1)/r!
Ω	1.0877683071982	Real period
R	3.296001995239	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31200bu4 62400gz4 93600t4 6240m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200be4

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 31200be4

-4	8	-3	5
31200bu4	62400gz4	93600t4	6240m3

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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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