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	15624j	Isogeny class
Conductor	15624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-28954998761472 = -1 · 211 · 37 · 7 · 314	Discriminant
Eigenvalues	2+ 3-  2 7+  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5181,-215458]	[a1,a2,a3,a4,a6]
Generators	[44890:327987:1000]	Generators of the group modulo torsion
j	10301655166/19393941	j-invariant
L	5.6393274297468	L(r)(E,1)/r!
Ω	0.34693787549893	Real period
R	8.1272870850969	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	31248r3 124992cb3 5208j4 109368o3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624j4

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	+	0	2	2	0	0	-6	-	-6	2	4	-12	-6	4	-14	12	0	-2	-4	4	-6	10

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Quadratic twists for elliptic curve 15624j4

-4	8	-3	-7
31248r3	124992cb3	5208j4	109368o3

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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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