Cremona's table of elliptic curves

35616 = 2⁵ · 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 53+	Signs for the Atkin-Lehner involutions
Class	35616i	Isogeny class
Conductor	35616	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	143360	Modular degree for the optimal curve
Δ	-23938451582976 = -1 · 212 · 38 · 75 · 53	Discriminant
Eigenvalues	2+ 3-  1 7-  5 -4  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-151005,22536747]	[a1,a2,a3,a4,a6]
Generators	[201:588:1]	Generators of the group modulo torsion
j	-92969527379908096/5844348531	j-invariant
L	8.0870474337351	L(r)(E,1)/r!
Ω	0.63916966948657	Real period
R	0.15815533456538	Regulator
r	1	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35616m1 71232t1 106848bj1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 35616i1

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	-	5	-4	0	-5	2	-3	-3	-3	-3	4	2	+	-12	-1	14	12	-14	2	-7	-6	10

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Quadratic twists for elliptic curve 35616i1

-4	8	-3
35616m1	71232t1	106848bj1

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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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