Cremona's table of elliptic curves

1870 = 2 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+ 17-	Signs for the Atkin-Lehner involutions
Class	1870b	Isogeny class
Conductor	1870	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-470570890625000 = -1 · 23 · 59 · 116 · 17	Discriminant
Eigenvalues	2+  1 5+ -4 11+  5 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-16869,1340376]	[a1,a2,a3,a4,a6]
j	-530829093701949769/470570890625000	j-invariant
L	0.96153161092673	L(r)(E,1)/r!
Ω	0.48076580546337	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	14960k2 59840s2 16830cx2 9350t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1870b2

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	+	-4	+	5	-	-1	0	9	-7	8	0	-10	3	-3	9	11	8	9	11	8	6	15	-13

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Quadratic twists for elliptic curve 1870b2

-4	8	-3	5	-7	-11	17
14960k2	59840s2	16830cx2	9350t2	91630v2	20570h2	31790k2

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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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