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	31200cf	Isogeny class
Conductor	31200	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	460800	Modular degree for the optimal curve
Δ	-30705480000000000 = -1 · 212 · 310 · 510 · 13	Discriminant
Eigenvalues	2- 3- 5+ -3  3 13-  7  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-490833,-132789537]	[a1,a2,a3,a4,a6]
j	-326938350400/767637	j-invariant
L	3.6069070161388	L(r)(E,1)/r!
Ω	0.09017267540349	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31200i1 62400r1 93600bv1 31200k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200cf1

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
-	-	+	-3	3	-	7	8	-4	-3	11	0	-2	8	9	9	9	1	-5	0	-12	8	9	12	10

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Quadratic twists for elliptic curve 31200cf1

-4	8	-3	5
31200i1	62400r1	93600bv1	31200k1

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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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