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	470d	Isogeny class
Conductor	470	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	51911500 = 22 · 53 · 473	Discriminant
Eigenvalues	2-  1 5+  5 -3  5  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-176,-844]	[a1,a2,a3,a4,a6]
j	603136942849/51911500	j-invariant
L	2.6358129074108	L(r)(E,1)/r!
Ω	1.3179064537054	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	3760i2 15040j2 4230o2 2350c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470d2

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	+	5	-3	5	0	-7	6	-6	5	8	-6	-10	+	-6	-12	-1	2	0	-13	-16	9	6	2

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Quadratic twists for elliptic curve 470d2

-4	8	-3	5	-7	-11	13	-47
3760i2	15040j2	4230o2	2350c2	23030x2	56870d2	79430g2	22090o2

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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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