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	96	Product of Tamagawa factors cp
Δ	213206722560000 = 214 · 36 · 54 · 134	Discriminant
Eigenvalues	2+ 3- 5+  0  4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-608401,182451599]	[a1,a2,a3,a4,a6]
j	1520107298839022416/13013105625	j-invariant
L	3.0323391503285	L(r)(E,1)/r!
Ω	0.50538985838809	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	12480bm2 1560j2 37440cc2 62400v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480t2

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 12480t2

-4	8	-3	5
12480bm2	1560j2	37440cc2	62400v2

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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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