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	12480bf	Isogeny class
Conductor	12480	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-19741363200 = -1 · 210 · 33 · 52 · 134	Discriminant
Eigenvalues	2+ 3- 5-  0  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,675,675]	[a1,a2,a3,a4,a6]
Generators	[15:120:1]	Generators of the group modulo torsion
j	33165879296/19278675	j-invariant
L	5.890234708789	L(r)(E,1)/r!
Ω	0.73375651202316	Real period
R	1.3379176453117	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	12480bz1 1560i1 37440bc1 62400u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480bf1

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

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Quadratic twists for elliptic curve 12480bf1

-4	8	-3	5
12480bz1	1560i1	37440bc1	62400u1

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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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