Cremona's table of elliptic curves

68672 = 2⁶ · 29 · 37

Field	Data	Notes
Atkin-Lehner	2+ 29- 37-	Signs for the Atkin-Lehner involutions
Class	68672n	Isogeny class
Conductor	68672	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	697944850432 = 214 · 292 · 373	Discriminant
Eigenvalues	2+ -1 -4  5 -3 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8325,292381]	[a1,a2,a3,a4,a6]
Generators	[124:1073:1]	Generators of the group modulo torsion
j	3895010796544/42599173	j-invariant
L	3.6412562254512	L(r)(E,1)/r!
Ω	0.9086339198315	Real period
R	0.66789938658362	Regulator
r	1	Rank of the group of rational points
S	0.99999999981985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	68672bg1 8584d1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 68672n1

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
+	-1	-4	5	-3	-2	0	0	4	-	-6	-	-3	8	3	-5	14	0	-12	3	-7	-8	-15	-6	-4

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Quadratic twists for elliptic curve 68672n1

-4	8
68672bg1	8584d1

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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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