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	3857b	Isogeny class
Conductor	3857	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	-155741544581 = -1 · 72 · 194 · 293	Discriminant
Eigenvalues	-1 -1 -3 7- -5  3 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4332,109570]	[a1,a2,a3,a4,a6]
Generators	[-70:310:1] [46:-125:1]	Generators of the group modulo torsion
j	-8990737580405953/155741544581	j-invariant
L	2.315929847671	L(r)(E,1)/r!
Ω	1.0269628961978	Real period
R	0.093963547605853	Regulator
r	2	Rank of the group of rational points
S	0.99999999999966	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	61712f1 34713l1 96425c1 26999j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3857b1

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	-3	-	-5	3	-4	-	-6	-	-9	-2	-4	-1	-5	-9	-4	-14	2	-8	-8	3	-12	-14	-8

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Quadratic twists for elliptic curve 3857b1

-4	-3	5	-7	-19	29
61712f1	34713l1	96425c1	26999j1	73283h1	111853f1

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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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