Cremona's table of elliptic curves

15624 = 2³ · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 31+	Signs for the Atkin-Lehner involutions
Class	15624g	Isogeny class
Conductor	15624	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	8747440128 = 211 · 39 · 7 · 31	Discriminant
Eigenvalues	2+ 3-  2 7+ -4 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2249859,1298915998]	[a1,a2,a3,a4,a6]
j	843591384940292354/5859	j-invariant
L	1.2791984385736	L(r)(E,1)/r!
Ω	0.6395992192868	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31248w4 124992bk4 5208l3 109368x4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624g3

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

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Quadratic twists for elliptic curve 15624g3

-4	8	-3	-7
31248w4	124992bk4	5208l3	109368x4

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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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