Cremona's table of elliptic curves

3857 = 7 · 19 · 29

Field	Data	Notes
Atkin-Lehner	7+ 19- 29-	Signs for the Atkin-Lehner involutions
Class	3857a	Isogeny class
Conductor	3857	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-185186141 = -1 · 72 · 194 · 29	Discriminant
Eigenvalues	1 -3  1 7+ -3 -1  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-364,-2663]	[a1,a2,a3,a4,a6]
Generators	[32:117:1]	Generators of the group modulo torsion
j	-5341937695641/185186141	j-invariant
L	2.5132440205576	L(r)(E,1)/r!
Ω	0.54532344023088	Real period
R	0.57609022351339	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	61712k1 34713f1 96425j1 26999h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3857a1

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	-3	1	+	-3	-1	4	-	6	-	-3	6	0	1	1	-1	-8	10	2	0	4	-11	0	-6	-12

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Quadratic twists for elliptic curve 3857a1

-4	-3	5	-7	-19	29
61712k1	34713f1	96425j1	26999h1	73283b1	111853a1

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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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