Cremona's table of elliptic curves

213 = 3 · 71

Field	Data	Notes
Atkin-Lehner	3- 71+	Signs for the Atkin-Lehner involutions
Class	213a	Isogeny class
Conductor	213	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	15123 = 3 · 712	Discriminant
Eigenvalues	1 3-  2  2  0 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15,19]	[a1,a2,a3,a4,a6]
j	338608873/15123	j-invariant
L	1.9481162183251	L(r)(E,1)/r!
Ω	3.8962324366501	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	3408f2 13632c2 639a2 5325a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 213a2

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	-	2	2	0	-2	0	0	0	-2	-10	-6	0	-4	12	-4	12	10	2	+	-10	4	-4	6	-2

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Quadratic twists for elliptic curve 213a2

-4	8	-3	5	-7	-11	13	17	-19	-23	-71
3408f2	13632c2	639a2	5325a2	10437a2	25773t2	35997a2	61557a2	76893e2	112677c2	15123a2

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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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