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	12480u	Isogeny class
Conductor	12480	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-65431142400 = -1 · 226 · 3 · 52 · 13	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,959,4895]	[a1,a2,a3,a4,a6]
j	371694959/249600	j-invariant
L	1.3858073744606	L(r)(E,1)/r!
Ω	0.6929036872303	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12480bl1 390b1 37440cb1 62400z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480u1

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	+	-6	-4	8	-6	-8	10	-6	-4	0	10	-4	2	12	16	2	-16	12	10	-6

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Quadratic twists for elliptic curve 12480u1

-4	8	-3	5
12480bl1	390b1	37440cb1	62400z1

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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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