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	31200d	Isogeny class
Conductor	31200	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	12480000000 = 212 · 3 · 57 · 13	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-26033,-1608063]	[a1,a2,a3,a4,a6]
j	30488290624/195	j-invariant
L	1.503409422688	L(r)(E,1)/r!
Ω	0.37585235567225	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31200cb4 62400ca1 93600dt4 6240ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200d4

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

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Quadratic twists for elliptic curve 31200d4

-4	8	-3	5
31200cb4	62400ca1	93600dt4	6240ba2

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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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