Cremona's table of elliptic curves

3172 = 2² · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 13+ 61-	Signs for the Atkin-Lehner involutions
Class	3172a	Isogeny class
Conductor	3172	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	82253821478608 = 24 · 135 · 614	Discriminant
Eigenvalues	2-  0  2  2 -6 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-122524,16501677]	[a1,a2,a3,a4,a6]
Generators	[25557:957090:343]	Generators of the group modulo torsion
j	12713561533627711488/5140863842413	j-invariant
L	3.7075954179463	L(r)(E,1)/r!
Ω	0.59786365144424	Real period
R	6.2014063055848	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	12688d1 50752c1 28548d1 79300e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3172a1

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

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Quadratic twists for elliptic curve 3172a1

-4	8	-3	5	13
12688d1	50752c1	28548d1	79300e1	41236d1

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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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