Cremona's table of elliptic curves

62400 = 2⁶ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	62400ep	Isogeny class
Conductor	62400	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	5922408960000000000 = 218 · 34 · 510 · 134	Discriminant
Eigenvalues	2- 3+ 5+  0  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-832033,267903937]	[a1,a2,a3,a4,a6]
Generators	[-627:23296:1]	Generators of the group modulo torsion
j	15551989015681/1445900625	j-invariant
L	5.9302480811757	L(r)(E,1)/r!
Ω	0.23307825502098	Real period
R	3.1803954003008	Regulator
r	1	Rank of the group of rational points
S	0.99999999995699	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	62400cs4 15600bz3 12480cj3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 62400ep4

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	-	-2	-4	8	2	8	6	-6	4	-8	6	-12	2	4	0	6	-16	4	10	-18

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Quadratic twists for elliptic curve 62400ep4

-4	8	5
62400cs4	15600bz3	12480cj3

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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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