Cremona's table of elliptic curves

870 = 2 · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 29-	Signs for the Atkin-Lehner involutions
Class	870b	Isogeny class
Conductor	870	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	12848183733600 = 25 · 33 · 52 · 296	Discriminant
Eigenvalues	2+ 3- 5+  2 -6 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7149,-156728]	[a1,a2,a3,a4,a6]
Generators	[-70:78:1]	Generators of the group modulo torsion
j	40399154288735689/12848183733600	j-invariant
L	1.9885607214778	L(r)(E,1)/r!
Ω	0.53224635238293	Real period
R	3.7361659926362	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	6960w2 27840w2 2610m2 4350s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870b2

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
+	-	+	2	-6	-4	-6	-4	0	-	2	2	0	-4	0	6	-12	-4	8	0	2	-10	18	0	-10

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Quadratic twists for elliptic curve 870b2

-4	8	-3	5	-7	-11	29
6960w2	27840w2	2610m2	4350s2	42630bb2	105270bt2	25230o2

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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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