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	12480y	Isogeny class
Conductor	12480	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-3194880 = -1 · 214 · 3 · 5 · 13	Discriminant
Eigenvalues	2+ 3- 5+ -5 -1 13+ -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1381,-20221]	[a1,a2,a3,a4,a6]
j	-17790954496/195	j-invariant
L	0.39155669165324	L(r)(E,1)/r!
Ω	0.39155669165324	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12480br1 1560l1 37440cm1 62400bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480y1

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
+	-	+	-5	-1	+	-3	-6	-7	-6	-2	-1	7	-8	2	-13	8	7	-12	1	-10	3	-8	13	7

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Quadratic twists for elliptic curve 12480y1

-4	8	-3	5
12480br1	1560l1	37440cm1	62400bj1

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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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