Cremona's table of elliptic curves

1392 = 2⁴ · 3 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 29-	Signs for the Atkin-Lehner involutions
Class	1392g	Isogeny class
Conductor	1392	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-853419888 = -1 · 24 · 37 · 293	Discriminant
Eigenvalues	2+ 3- -2 -3  5  1 -7 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,56,1415]	[a1,a2,a3,a4,a6]
Generators	[17:87:1]	Generators of the group modulo torsion
j	1192310528/53338743	j-invariant
L	2.7872884193279	L(r)(E,1)/r!
Ω	1.1997743525655	Real period
R	0.11062748564693	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	696f1 5568s1 4176f1 34800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1392g1

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	-3	5	1	-7	-2	-4	-	4	-12	-6	8	-3	-14	2	-8	-5	-8	4	2	-14	15	14

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Quadratic twists for elliptic curve 1392g1

-4	8	-3	5	-7	29
696f1	5568s1	4176f1	34800k1	68208m1	40368d1

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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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