Cremona's table of elliptic curves

42320 = 2⁴ · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2- 5- 23-	Signs for the Atkin-Lehner involutions
Class	42320x	Isogeny class
Conductor	42320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-108339200 = -1 · 213 · 52 · 232	Discriminant
Eigenvalues	2- -1 5- -4  0 -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-360,2800]	[a1,a2,a3,a4,a6]
Generators	[-20:40:1] [12:8:1]	Generators of the group modulo torsion
j	-2387929/50	j-invariant
L	7.1147610332688	L(r)(E,1)/r!
Ω	1.8793076062714	Real period
R	0.47323020786535	Regulator
r	2	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5290c1 42320n1	Quadratic twists by: -4 -23

Hecke Eigenvalues for elliptic curve 42320x1

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	0	-4	-3	-1	-	-6	4	-2	-6	11	0	6	-3	-8	-13	12	-7	-10	-9	-6	-14

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Quadratic twists for elliptic curve 42320x1

-4	-23
5290c1	42320n1

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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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