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	62400fq	Isogeny class
Conductor	62400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-7118280000 = -1 · 26 · 34 · 54 · 133	Discriminant
Eigenvalues	2- 3+ 5- -3  5 13+ -5  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,4062]	[a1,a2,a3,a4,a6]
Generators	[11:72:1]	Generators of the group modulo torsion
j	-1600/177957	j-invariant
L	4.6858543167161	L(r)(E,1)/r!
Ω	1.0567528831955	Real period
R	2.217100322733	Regulator
r	1	Rank of the group of rational points
S	0.99999999998989	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	62400ht1 31200bb1 62400hj1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 62400fq1

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

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Quadratic twists for elliptic curve 62400fq1

-4	8	5
62400ht1	31200bb1	62400hj1

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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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