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	2	Product of Tamagawa factors cp
Δ	8709304483840 = 224 · 5 · 473	Discriminant
Eigenvalues	2+  1 5- -1  3  5  6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-6348,132618]	[a1,a2,a3,a4,a6]
j	28283693153853241/8709304483840	j-invariant
L	1.3582924068667	L(r)(E,1)/r!
Ω	0.67914620343333	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3760p2 15040b2 4230bb2 2350l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470b2

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 470b2

-4	8	-3	5	-7	-11	13	-47
3760p2	15040b2	4230bb2	2350l2	23030f2	56870x2	79430k2	22090a2

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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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