Cremona's table of elliptic curves

31311 = 3² · 7² · 71

Field	Data	Notes
Atkin-Lehner	3- 7+ 71+	Signs for the Atkin-Lehner involutions
Class	31311a	Isogeny class
Conductor	31311	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	34272	Modular degree for the optimal curve
Δ	298380334959 = 36 · 78 · 71	Discriminant
Eigenvalues	-1 3- -3 7+ -4  0 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1994,-21486]	[a1,a2,a3,a4,a6]
Generators	[86:618:1] [-31:114:1]	Generators of the group modulo torsion
j	208537/71	j-invariant
L	4.3758889019157	L(r)(E,1)/r!
Ω	0.73419883022585	Real period
R	0.99334783298633	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3479a1 31311d1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 31311a1

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	-	-3	+	-4	0	-4	-4	-3	-5	7	3	12	0	-3	4	-13	8	-3	+	-13	2	-6	-2	-10

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Quadratic twists for elliptic curve 31311a1

-3	-7
3479a1	31311d1

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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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