Cremona's table of elliptic curves

2170 = 2 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5- 7- 31-	Signs for the Atkin-Lehner involutions
Class	2170f	Isogeny class
Conductor	2170	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	2186668933120 = 221 · 5 · 7 · 313	Discriminant
Eigenvalues	2+  1 5- 7-  3 -1  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4418,-88172]	[a1,a2,a3,a4,a6]
j	9533657181184921/2186668933120	j-invariant
L	1.7857847592234	L(r)(E,1)/r!
Ω	0.59526158640779	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	17360bd2 69440s2 19530by2 10850t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170f2

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	-	-	3	-1	0	-1	3	6	-	8	-6	8	3	6	-9	8	-4	3	8	8	3	15	-13

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Quadratic twists for elliptic curve 2170f2

-4	8	-3	5	-7	-31
17360bd2	69440s2	19530by2	10850t2	15190c2	67270s2

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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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