Cremona's table of elliptic curves

335 = 5 · 67

Field	Data	Notes
Atkin-Lehner	5- 67-	Signs for the Atkin-Lehner involutions
Class	335a	Isogeny class
Conductor	335	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-1675 = -1 · 52 · 67	Discriminant
Eigenvalues	0  0 5- -2 -2 -2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-2,2]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-884736/1675	j-invariant
L	1.4976179638561	L(r)(E,1)/r!
Ω	4.2194745614714	Real period
R	0.177464983144	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	5360n1 21440c1 3015b1 1675a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 335a1

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	0	-	-2	-2	-2	-3	-1	-1	-9	0	-3	-2	6	9	12	5	0	-	-4	-1	-4	-4	3	-14

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Quadratic twists for elliptic curve 335a1

-4	8	-3	5	-7	-11	13	17	-19	-67
5360n1	21440c1	3015b1	1675a1	16415b1	40535j1	56615a1	96815a1	120935a1	22445a1

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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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