Cremona's table of elliptic curves

1520 = 2⁴ · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	1520a	Isogeny class
Conductor	1520	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	722000 = 24 · 53 · 192	Discriminant
Eigenvalues	2+  2 5-  0  4  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-35,-58]	[a1,a2,a3,a4,a6]
j	304900096/45125	j-invariant
L	2.9663595639438	L(r)(E,1)/r!
Ω	1.9775730426292	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	760d1 6080r1 13680h1 7600b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1520a1

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
+	2	-	0	4	4	-2	+	4	-6	8	-4	-2	-4	8	0	8	2	14	8	6	4	-16	-18	-4

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Quadratic twists for elliptic curve 1520a1

-4	8	-3	5	-7	-19
760d1	6080r1	13680h1	7600b1	74480n1	28880k1

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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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