Cremona's table of elliptic curves

2870 = 2 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 41+	Signs for the Atkin-Lehner involutions
Class	2870a	Isogeny class
Conductor	2870	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	803600 = 24 · 52 · 72 · 41	Discriminant
Eigenvalues	2+  0 5+ 7+  6  0  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-35,-59]	[a1,a2,a3,a4,a6]
Generators	[-3:5:1]	Generators of the group modulo torsion
j	4818245769/803600	j-invariant
L	2.2875225596149	L(r)(E,1)/r!
Ω	1.9824279289605	Real period
R	0.57694974081967	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22960k1 91840m1 25830bh1 14350q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870a1

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
+	0	+	+	6	0	0	-2	0	-6	-8	10	+	12	-12	8	8	-14	-4	-10	14	-10	4	-2	-12

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Quadratic twists for elliptic curve 2870a1

-4	8	-3	5	-7	41
22960k1	91840m1	25830bh1	14350q1	20090e1	117670g1

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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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