Cremona's table of elliptic curves

42432 = 2⁶ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	42432k	Isogeny class
Conductor	42432	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	12099613114368 = 214 · 32 · 136 · 17	Discriminant
Eigenvalues	2+ 3+  0  2  2 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6193,86833]	[a1,a2,a3,a4,a6]
Generators	[97:624:1]	Generators of the group modulo torsion
j	1603530178000/738501777	j-invariant
L	5.5425813070428	L(r)(E,1)/r!
Ω	0.6387123122744	Real period
R	0.72314525133007	Regulator
r	1	Rank of the group of rational points
S	0.99999999999916	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42432cn2 5304e2 127296s2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 42432k2

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	2	2	-	-	4	-8	-2	-6	-8	4	4	0	14	-8	10	12	-6	-8	4	-4	2	-12

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Quadratic twists for elliptic curve 42432k2

-4	8	-3
42432cn2	5304e2	127296s2

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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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