Cremona's table of elliptic curves

41664 = 2⁶ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	41664z	Isogeny class
Conductor	41664	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-3200923575779328 = -1 · 220 · 33 · 76 · 312	Discriminant
Eigenvalues	2+ 3+  0 7- -6 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,22687,2375649]	[a1,a2,a3,a4,a6]
Generators	[115:2548:1]	Generators of the group modulo torsion
j	4926016478375/12210554412	j-invariant
L	4.3437624567099	L(r)(E,1)/r!
Ω	0.31303635203445	Real period
R	2.3127039551347	Regulator
r	1	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41664dg2 1302h2 124992db2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41664z2

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	-	-6	-2	6	4	-6	0	-	-2	0	4	6	-12	-6	10	4	12	2	8	0	-18	-10

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Quadratic twists for elliptic curve 41664z2

-4	8	-3
41664dg2	1302h2	124992db2

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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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