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	12480cb	Isogeny class
Conductor	12480	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	1560000 = 26 · 3 · 54 · 13	Discriminant
Eigenvalues	2- 3+ 5-  0  4 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-60,-150]	[a1,a2,a3,a4,a6]
Generators	[11:20:1]	Generators of the group modulo torsion
j	379503424/24375	j-invariant
L	4.6685073812394	L(r)(E,1)/r!
Ω	1.719912708646	Real period
R	2.714386234703	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	12480cv1 6240m2 37440dv1 62400gz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480cb1

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

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Quadratic twists for elliptic curve 12480cb1

-4	8	-3	5
12480cv1	6240m2	37440dv1	62400gz1

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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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