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	15624l	Isogeny class
Conductor	15624	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	-2278782506585088 = -1 · 210 · 39 · 76 · 312	Discriminant
Eigenvalues	2+ 3-  0 7-  2 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26715,-2845978]	[a1,a2,a3,a4,a6]
Generators	[223:1512:1]	Generators of the group modulo torsion
j	-2824631270500/3052638603	j-invariant
L	5.2247544884005	L(r)(E,1)/r!
Ω	0.17907895427272	Real period
R	1.2156543160947	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31248j2 124992cl2 5208k2 109368q2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624l2

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

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Quadratic twists for elliptic curve 15624l2

-4	8	-3	-7
31248j2	124992cl2	5208k2	109368q2

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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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