Cremona's table of elliptic curves

3120 = 2⁴ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	3120r	Isogeny class
Conductor	3120	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	2433600000000 = 212 · 32 · 58 · 132	Discriminant
Eigenvalues	2- 3+ 5-  0 -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-130000,18084352]	[a1,a2,a3,a4,a6]
j	59319456301170001/594140625	j-invariant
L	1.4741163178477	L(r)(E,1)/r!
Ω	0.73705815892386	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	195a5 12480cj5 9360bm5 15600bz5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120r5

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	-2	8	6	-6	4	8	6	12	-2	4	0	-6	-16	4	10	18

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Quadratic twists for elliptic curve 3120r5

-4	8	-3	5	13
195a5	12480cj5	9360bm5	15600bz5	40560bg6

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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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