Cremona's table of elliptic curves

126324 = 2² · 3² · 11² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 29+	Signs for the Atkin-Lehner involutions
Class	126324a	Isogeny class
Conductor	126324	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	571200	Modular degree for the optimal curve
Δ	-15697476705710448 = -1 · 24 · 33 · 116 · 295	Discriminant
Eigenvalues	2- 3+  0 -1 11-  3  5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-41745,-6863967]	[a1,a2,a3,a4,a6]
Generators	[33705:152289:125]	Generators of the group modulo torsion
j	-10512288000/20511149	j-invariant
L	7.7535746971195	L(r)(E,1)/r!
Ω	0.15706311855036	Real period
R	8.2276633114916	Regulator
r	1	Rank of the group of rational points
S	0.99999999337183	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	126324c1 1044c1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 126324a1

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	-1	-	3	5	2	0	+	6	10	10	2	-5	-10	10	-4	-1	-10	0	4	0	-15	-6

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Quadratic twists for elliptic curve 126324a1

-3	-11
126324c1	1044c1

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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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