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	3813a	Isogeny class
Conductor	3813	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	75600	Modular degree for the optimal curve
Δ	2370761600280886557 = 37 · 319 · 41	Discriminant
Eigenvalues	0 3+ -2 -4 -4  5  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-621739,173752536]	[a1,a2,a3,a4,a6]
Generators	[8:12991:1]	Generators of the group modulo torsion
j	26579618406634046390272/2370761600280886557	j-invariant
L	1.6779032934016	L(r)(E,1)/r!
Ω	0.25183984256074	Real period
R	6.6625807749102	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	61008q1 11439e1 95325q1 118203g1	Quadratic twists by: -4 -3 5 -31

Hecke Eigenvalues for elliptic curve 3813a1

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	-4	-4	5	4	-2	-5	10	+	2	+	-2	7	4	6	6	16	-12	4	-11	7	0	-14

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Quadratic twists for elliptic curve 3813a1

-4	-3	5	-31
61008q1	11439e1	95325q1	118203g1

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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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