Cremona's table of elliptic curves

1470 = 2 · 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	1470l	Isogeny class
Conductor	1470	Conductor
∏ cp	390	Product of Tamagawa factors cp
deg	3120	Modular degree for the optimal curve
Δ	-553190400000 = -1 · 213 · 32 · 55 · 74	Discriminant
Eigenvalues	2- 3+ 5- 7+ -5 -5 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2990,71147]	[a1,a2,a3,a4,a6]
Generators	[27:-119:1]	Generators of the group modulo torsion
j	-1231272543361/230400000	j-invariant
L	3.4425498706978	L(r)(E,1)/r!
Ω	0.88588471246845	Real period
R	0.0099641079999126	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11760cm1 47040cb1 4410g1 7350v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1470l1

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	-5	-4	-7	1	0	-2	1	5	12	-11	-9	4	4	-12	2	10	-12	-12	14	-8

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Quadratic twists for elliptic curve 1470l1

-4	8	-3	5	-7
11760cm1	47040cb1	4410g1	7350v1	1470q1

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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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