Cremona's table of elliptic curves

31605 = 3 · 5 · 7² · 43

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 43+	Signs for the Atkin-Lehner involutions
Class	31605r	Isogeny class
Conductor	31605	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	3414762225 = 33 · 52 · 76 · 43	Discriminant
Eigenvalues	1 3- 5+ 7- -2 -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1104,-13919]	[a1,a2,a3,a4,a6]
Generators	[-146:189:8]	Generators of the group modulo torsion
j	1263214441/29025	j-invariant
L	6.4972038170556	L(r)(E,1)/r!
Ω	0.82949171722783	Real period
R	2.6109176990014	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	94815bg1 645b1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 31605r1

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	-	+	-	-2	-2	0	-6	0	10	-8	-4	10	+	0	12	6	10	12	4	8	-16	12	10	-6

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Quadratic twists for elliptic curve 31605r1

-3	-7
94815bg1	645b1

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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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