Cremona's table of elliptic curves

35040 = 2⁵ · 3 · 5 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 73-	Signs for the Atkin-Lehner involutions
Class	35040b	Isogeny class
Conductor	35040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6528	Modular degree for the optimal curve
Δ	-1681920 = -1 · 29 · 32 · 5 · 73	Discriminant
Eigenvalues	2+ 3+ 5+ -2 -6 -4  1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,24,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1] [8:26:1]	Generators of the group modulo torsion
j	2863288/3285	j-invariant
L	6.4442214695085	L(r)(E,1)/r!
Ω	1.7722147976434	Real period
R	0.90906326339192	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35040p1 70080bd1 105120bd1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 35040b1

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	-4	1	-1	9	-3	3	3	-9	-1	-12	-12	-6	-6	-10	0	-	6	16	11	-10

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Quadratic twists for elliptic curve 35040b1

-4	8	-3
35040p1	70080bd1	105120bd1

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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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