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	15624w	Isogeny class
Conductor	15624	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	-4007918354189347584 = -1 · 28 · 313 · 73 · 315	Discriminant
Eigenvalues	2- 3-  3 7+  0  3  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,83364,95873668]	[a1,a2,a3,a4,a6]
j	343314268285952/21475899960291	j-invariant
L	3.7698766182787	L(r)(E,1)/r!
Ω	0.18849383091393	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31248t1 124992ch1 5208e1 109368bs1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624w1

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	+	0	3	4	6	9	-1	-	10	-5	12	8	9	-4	-15	-13	6	-13	8	6	-16	-10

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Quadratic twists for elliptic curve 15624w1

-4	8	-3	-7
31248t1	124992ch1	5208e1	109368bs1

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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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