Cremona's table of elliptic curves

19344 = 2⁴ · 3 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 31-	Signs for the Atkin-Lehner involutions
Class	19344c	Isogeny class
Conductor	19344	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-606819790512 = -1 · 24 · 35 · 132 · 314	Discriminant
Eigenvalues	2+ 3+  0 -4  6 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4083,108558]	[a1,a2,a3,a4,a6]
j	-470596000000000/37926236907	j-invariant
L	1.7945312982137	L(r)(E,1)/r!
Ω	0.89726564910686	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9672c1 77376br1 58032h1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19344c1

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
+	+	0	-4	6	+	6	4	-4	6	-	6	8	4	-2	-6	6	2	-8	14	14	8	-18	0	6

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Quadratic twists for elliptic curve 19344c1

-4	8	-3
9672c1	77376br1	58032h1

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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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