Cremona's table of elliptic curves

357 = 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	357d	Isogeny class
Conductor	357	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-1821771 = -1 · 37 · 72 · 17	Discriminant
Eigenvalues	-2 3- -3 7- -3  1 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-42,110]	[a1,a2,a3,a4,a6]
Generators	[0:10:1]	Generators of the group modulo torsion
j	-8390176768/1821771	j-invariant
L	1.0297863325531	L(r)(E,1)/r!
Ω	2.5259384792794	Real period
R	0.029120331795222	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	5712l1 22848n1 1071d1 8925g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 357d1

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
-2	-	-3	-	-3	1	+	-7	1	-10	4	-10	3	-11	-8	-4	4	10	-8	8	-2	16	6	-8	-4

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Quadratic twists for elliptic curve 357d1

-4	8	-3	5	-7	-11	13	17	-19
5712l1	22848n1	1071d1	8925g1	2499g1	43197m1	60333i1	6069a1	128877i1

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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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