Cremona's table of elliptic curves

42900 = 2² · 3 · 5² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 11- 13-	Signs for the Atkin-Lehner involutions
Class	42900t	Isogeny class
Conductor	42900	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	5342827213152000 = 28 · 312 · 53 · 11 · 134	Discriminant
Eigenvalues	2- 3+ 5-  2 11- 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-205628,35785752]	[a1,a2,a3,a4,a6]
Generators	[206:1458:1]	Generators of the group modulo torsion
j	30048486370938128/166963350411	j-invariant
L	5.7760669387431	L(r)(E,1)/r!
Ω	0.43176792895986	Real period
R	1.1148093206487	Regulator
r	1	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	128700bt2 42900bo2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 42900t2

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	-	-	-6	4	8	6	-4	4	6	-2	0	-4	0	-6	8	-12	-14	-16	-10	-14	16

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Quadratic twists for elliptic curve 42900t2

-3	5
128700bt2	42900bo2

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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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