Cremona's table of elliptic curves

3813 = 3 · 31 · 41

Field	Data	Notes
Atkin-Lehner	3- 31+ 41-	Signs for the Atkin-Lehner involutions
Class	3813c	Isogeny class
Conductor	3813	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	238739377692681 = 38 · 316 · 41	Discriminant
Eigenvalues	1 3-  2 -2  0  0  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15535,-53659]	[a1,a2,a3,a4,a6]
Generators	[-23:551:1]	Generators of the group modulo torsion
j	414588544294108393/238739377692681	j-invariant
L	5.2700321279757	L(r)(E,1)/r!
Ω	0.46552944473963	Real period
R	2.8301282483449	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	61008j1 11439c1 95325f1 118203d1	Quadratic twists by: -4 -3 5 -31

Hecke Eigenvalues for elliptic curve 3813c1

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	-2	0	0	0	-6	0	-4	+	2	-	-4	-6	0	0	-6	-2	-6	-14	4	-4	8	-18

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Quadratic twists for elliptic curve 3813c1

-4	-3	5	-31
61008j1	11439c1	95325f1	118203d1

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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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