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	735f	Isogeny class
Conductor	735	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-3281866875 = -1 · 37 · 54 · 74	Discriminant
Eigenvalues	-2 3- 5- 7+ -6 -3 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-310,3364]	[a1,a2,a3,a4,a6]
Generators	[-19:52:1]	Generators of the group modulo torsion
j	-1376628736/1366875	j-invariant
L	1.4518853833407	L(r)(E,1)/r!
Ω	1.2882643756245	Real period
R	0.013416772309097	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	11760bu1 47040c1 2205e1 3675c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 735f1

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
-2	-	-	+	-6	-3	-4	1	-4	-8	1	7	-6	1	2	4	-8	-14	7	6	1	-1	2	-12	-6

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Quadratic twists for elliptic curve 735f1

-4	8	-3	5	-7	-11	13
11760bu1	47040c1	2205e1	3675c1	735b1	88935bx1	124215bu1

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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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