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	12480b	Isogeny class
Conductor	12480	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-4.1742035358749E+20	Discriminant
Eigenvalues	2+ 3+ 5+  2  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3416161,-2620405535]	[a1,a2,a3,a4,a6]
Generators	[23195839668623163777015123:-1625863671735848789497348096:4137181472045403529307]	Generators of the group modulo torsion
j	-16818951115904497561/1592332281446400	j-invariant
L	3.8342226684885	L(r)(E,1)/r!
Ω	0.055227293504047	Real period
R	34.713113980568	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12480cm3 390d3 37440cd3 62400cy3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480b3

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	0	+	0	-2	-6	0	8	-2	6	4	0	6	0	-14	4	0	-4	-16	12	-6	-4

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Quadratic twists for elliptic curve 12480b3

-4	8	-3	5
12480cm3	390d3	37440cd3	62400cy3

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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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