Cremona's table of elliptic curves

12480 = 2⁶ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	12480cj	Isogeny class
Conductor	12480	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	379034173440000 = 218 · 34 · 54 · 134	Discriminant
Eigenvalues	2- 3- 5+  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33281,2129919]	[a1,a2,a3,a4,a6]
Generators	[-113:2112:1]	Generators of the group modulo torsion
j	15551989015681/1445900625	j-invariant
L	5.5055601665905	L(r)(E,1)/r!
Ω	0.52117882230393	Real period
R	2.6409170571496	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12480a3 3120r3 37440ex4 62400ep4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480cj3

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 12480cj3

-4	8	-3	5
12480a3	3120r3	37440ex4	62400ep4

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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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