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	15624o	Isogeny class
Conductor	15624	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	364476672 = 28 · 38 · 7 · 31	Discriminant
Eigenvalues	2+ 3-  0 7-  2 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-615,-5798]	[a1,a2,a3,a4,a6]
j	137842000/1953	j-invariant
L	1.9190368897975	L(r)(E,1)/r!
Ω	0.95951844489873	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31248i1 124992da1 5208n1 109368k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624o1

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	-6	-2	4	6	-4	-	2	0	-4	6	0	6	-2	-12	0	-6	16	8	14	-18

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Quadratic twists for elliptic curve 15624o1

-4	8	-3	-7
31248i1	124992da1	5208n1	109368k1

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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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