Cremona's table of elliptic curves

356 = 2² · 89

Field	Data	Notes
Atkin-Lehner	2- 89-	Signs for the Atkin-Lehner involutions
Class	356a	Isogeny class
Conductor	356	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-22784 = -1 · 28 · 89	Discriminant
Eigenvalues	2- -1 -1  0  0 -4 -1 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4,-8]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	21296/89	j-invariant
L	1.473836667143	L(r)(E,1)/r!
Ω	1.9261487705605	Real period
R	0.25505760331519	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	1424d1 5696e1 3204c1 8900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 356a1

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	0	0	-4	-1	-5	-1	-6	3	-6	2	1	10	9	4	-4	-2	2	7	2	-4	-	1

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Quadratic twists for elliptic curve 356a1

-4	8	-3	5	-7	-11	13	17	-19	89
1424d1	5696e1	3204c1	8900b1	17444a1	43076a1	60164a1	102884a1	128516d1	31684a1

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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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