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	31200w	Isogeny class
Conductor	31200	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	-25022177856000000 = -1 · 212 · 34 · 56 · 136	Discriminant
Eigenvalues	2+ 3- 5+  2  2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-62433,9673263]	[a1,a2,a3,a4,a6]
Generators	[-177:3900:1]	Generators of the group modulo torsion
j	-420526439488/390971529	j-invariant
L	7.5619824182421	L(r)(E,1)/r!
Ω	0.34469654490513	Real period
R	0.22852172832687	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31200bp2 62400i1 93600ee2 1248f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200w2

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	2	-	-6	-2	0	2	2	-10	2	-8	2	2	10	6	-14	-14	6	-4	-6	10	-10

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Quadratic twists for elliptic curve 31200w2

-4	8	-3	5
31200bp2	62400i1	93600ee2	1248f2

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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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