Cremona's table of elliptic curves

78144 = 2⁶ · 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 37+	Signs for the Atkin-Lehner involutions
Class	78144c	Isogeny class
Conductor	78144	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	539591196672 = 214 · 37 · 11 · 372	Discriminant
Eigenvalues	2+ 3+  0 -4 11+  0  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-32273,2242065]	[a1,a2,a3,a4,a6]
Generators	[-191:1184:1]	Generators of the group modulo torsion
j	226900390642000/32934033	j-invariant
L	4.4791861635765	L(r)(E,1)/r!
Ω	0.89261957609403	Real period
R	2.5090118372957	Regulator
r	1	Rank of the group of rational points
S	0.99999999962783	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	78144cx1 9768q1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 78144c1

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

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Quadratic twists for elliptic curve 78144c1

-4	8
78144cx1	9768q1

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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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