Cremona's table of elliptic curves

3822 = 2 · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	3822ba	Isogeny class
Conductor	3822	Conductor
∏ cp	510	Product of Tamagawa factors cp
deg	85680	Modular degree for the optimal curve
Δ	-4026079379060260704 = -1 · 25 · 317 · 78 · 132	Discriminant
Eigenvalues	2- 3- -1 7+ -1 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-69336,96787872]	[a1,a2,a3,a4,a6]
Generators	[396:-11664:1]	Generators of the group modulo torsion
j	-6394640503489/698390001504	j-invariant
L	5.6509902064885	L(r)(E,1)/r!
Ω	0.20301800036594	Real period
R	0.054578278447855	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	30576bh1 122304d1 11466k1 95550f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822ba1

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	+	-1	+	-6	-4	-6	3	-11	4	12	-8	-8	-5	-5	12	16	6	-10	7	-17	-12	13

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Quadratic twists for elliptic curve 3822ba1

-4	8	-3	5	-7	13
30576bh1	122304d1	11466k1	95550f1	3822u1	49686y1

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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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