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	62400gj	Isogeny class
Conductor	62400	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	2554695936000000000 = 217 · 310 · 59 · 132	Discriminant
Eigenvalues	2- 3- 5+  2  4 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-428033,75384063]	[a1,a2,a3,a4,a6]
Generators	[778:-14625:1]	Generators of the group modulo torsion
j	4234737878642/1247410125	j-invariant
L	9.2285888548255	L(r)(E,1)/r!
Ω	0.23853629319891	Real period
R	0.96721013926306	Regulator
r	1	Rank of the group of rational points
S	1.0000000000278	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	62400m2 15600i2 12480bx2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 62400gj2

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	4	+	0	2	-2	-4	-4	-2	-6	4	8	-2	4	2	-8	-8	4	-8	-12	6	-4

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Quadratic twists for elliptic curve 62400gj2

-4	8	5
62400m2	15600i2	12480bx2

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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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