Cremona's table of elliptic curves

3848 = 2³ · 13 · 37

Field	Data	Notes
Atkin-Lehner	2+ 13- 37+	Signs for the Atkin-Lehner involutions
Class	3848a	Isogeny class
Conductor	3848	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2432	Modular degree for the optimal curve
Δ	270529792 = 28 · 134 · 37	Discriminant
Eigenvalues	2+ -1 -2 -3 -3 13- -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4089,102013]	[a1,a2,a3,a4,a6]
Generators	[-29:442:1] [-3:338:1]	Generators of the group modulo torsion
j	29542094605312/1056757	j-invariant
L	3.3523716307752	L(r)(E,1)/r!
Ω	1.6291937096785	Real period
R	0.1286054725591	Regulator
r	2	Rank of the group of rational points
S	0.99999999999965	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7696b1 30784e1 34632p1 96200t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3848a1

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	-2	-3	-3	-	-4	-4	-6	-6	0	+	3	-10	-3	-3	-12	0	8	-13	11	8	-9	12	-16

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Quadratic twists for elliptic curve 3848a1

-4	8	-3	5	13
7696b1	30784e1	34632p1	96200t1	50024d1

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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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