Cremona's table of elliptic curves

355 = 5 · 71

Field	Data	Notes
Atkin-Lehner	5- 71+	Signs for the Atkin-Lehner involutions
Class	355a	Isogeny class
Conductor	355	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-8875 = -1 · 53 · 71	Discriminant
Eigenvalues	0 -2 5- -1  0  5  6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,5,-1]	[a1,a2,a3,a4,a6]
j	11239424/8875	j-invariant
L	0.76309280897321	L(r)(E,1)/r!
Ω	2.2892784269196	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5680k1 22720c1 3195b1 1775a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 355a1

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	-2	-	-1	0	5	6	-1	0	-3	2	8	6	2	3	-3	-6	2	-4	+	-4	-1	6	15	-7

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Quadratic twists for elliptic curve 355a1

-4	8	-3	5	-7	-11	13	17	-19	-71
5680k1	22720c1	3195b1	1775a1	17395c1	42955d1	59995b1	102595a1	128155c1	25205c1

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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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