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	15624q	Isogeny class
Conductor	15624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8704	Modular degree for the optimal curve
Δ	-4115736576 = -1 · 211 · 33 · 74 · 31	Discriminant
Eigenvalues	2- 3+ -3 7+  1  1 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-699,-7754]	[a1,a2,a3,a4,a6]
Generators	[74:588:1]	Generators of the group modulo torsion
j	-683064198/74431	j-invariant
L	3.6900836235007	L(r)(E,1)/r!
Ω	0.46141169936982	Real period
R	1.9993444187374	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31248f1 124992k1 15624b1 109368bg1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624q1

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
-	+	-3	+	1	1	-3	5	6	-10	-	2	-12	0	3	-12	10	1	3	15	-12	3	-5	6	13

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Quadratic twists for elliptic curve 15624q1

-4	8	-3	-7
31248f1	124992k1	15624b1	109368bg1

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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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