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	357a	Isogeny class
Conductor	357	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	544	Modular degree for the optimal curve
Δ	-5271114033171 = -1 · 317 · 74 · 17	Discriminant
Eigenvalues	0 3+  1 7+  3  3 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,3565,72914]	[a1,a2,a3,a4,a6]
j	5009339741732864/5271114033171	j-invariant
L	1.0119618918739	L(r)(E,1)/r!
Ω	0.50598094593695	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5712z1 22848bb1 1071a1 8925x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 357a1

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	+	1	+	3	3	-	3	7	-6	10	4	-9	9	6	-10	-2	0	-12	-12	6	10	10	-4	8

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Quadratic twists for elliptic curve 357a1

-4	8	-3	5	-7	-11	13	17	-19
5712z1	22848bb1	1071a1	8925x1	2499j1	43197g1	60333c1	6069e1	128877n1

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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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