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	2870c	Isogeny class
Conductor	2870	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	12059022500 = 22 · 54 · 76 · 41	Discriminant
Eigenvalues	2+ -2 5+ 7-  6 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-100509,12256196]	[a1,a2,a3,a4,a6]
j	112287744132511049929/12059022500	j-invariant
L	0.65304915988419	L(r)(E,1)/r!
Ω	0.97957373982629	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	22960i1 91840t1 25830bl1 14350l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870c1

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

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Quadratic twists for elliptic curve 2870c1

-4	8	-3	5	-7	41
22960i1	91840t1	25830bl1	14350l1	20090f1	117670b1

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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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