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	12480t	Isogeny class
Conductor	12480	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	2299226342400000000 = 216 · 312 · 58 · 132	Discriminant
Eigenvalues	2+ 3- 5+  0  4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-621921,173904255]	[a1,a2,a3,a4,a6]
j	405929061432816484/35083409765625	j-invariant
L	3.0323391503285	L(r)(E,1)/r!
Ω	0.25269492919405	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12480bm4 1560j3 37440cc3 62400v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480t3

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

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Quadratic twists for elliptic curve 12480t3

-4	8	-3	5
12480bm4	1560j3	37440cc3	62400v3

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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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