Cremona's table of elliptic curves

470 = 2 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 5- 47+	Signs for the Atkin-Lehner involutions
Class	470b	Isogeny class
Conductor	470	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	1504000 = 28 · 53 · 47	Discriminant
Eigenvalues	2+  1 5- -1  3  5  6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5773,168328]	[a1,a2,a3,a4,a6]
j	21272583599722441/1504000	j-invariant
L	1.3582924068667	L(r)(E,1)/r!
Ω	2.0374386103	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	3760p1 15040b1 4230bb1 2350l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470b1

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
+	1	-	-1	3	5	6	-1	0	-6	5	8	0	8	+	0	-6	5	-4	-12	5	2	-15	6	-16

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Quadratic twists for elliptic curve 470b1

-4	8	-3	5	-7	-11	13	-47
3760p1	15040b1	4230bb1	2350l1	23030f1	56870x1	79430k1	22090a1

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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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