Cremona's table of elliptic curves

735 = 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	735a	Isogeny class
Conductor	735	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1297080225 = 32 · 52 · 78	Discriminant
Eigenvalues	1 3+ 5+ 7-  0  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-368,1947]	[a1,a2,a3,a4,a6]
j	47045881/11025	j-invariant
L	1.437375972542	L(r)(E,1)/r!
Ω	1.437375972542	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11760ce2 47040df2 2205k2 3675l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 735a2

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	+	+	-	0	6	-2	8	8	-2	-4	-2	6	4	-8	10	-4	2	4	-12	2	8	4	6	18

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Quadratic twists for elliptic curve 735a2

-4	8	-3	5	-7	-11	13
11760ce2	47040df2	2205k2	3675l2	105a2	88935p2	124215be2

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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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