Cremona's table of elliptic curves

19296 = 2⁵ · 3² · 67

Field	Data	Notes
Atkin-Lehner	2+ 3- 67-	Signs for the Atkin-Lehner involutions
Class	19296g	Isogeny class
Conductor	19296	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-8082661552128 = -1 · 212 · 38 · 673	Discriminant
Eigenvalues	2+ 3- -2 -2  4  4  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,136784]	[a1,a2,a3,a4,a6]
Generators	[-40:268:1]	Generators of the group modulo torsion
j	512/2706867	j-invariant
L	4.3539242048819	L(r)(E,1)/r!
Ω	0.5854868611969	Real period
R	0.61970138208016	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	19296o1 38592o1 6432l1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19296g1

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	-2	4	4	3	-5	-3	-5	8	7	-2	-4	-1	-4	5	-6	-	8	-15	2	0	-13	-2

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Quadratic twists for elliptic curve 19296g1

-4	8	-3
19296o1	38592o1	6432l1

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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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