Cremona's table of elliptic curves

15210 = 2 · 3² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	15210j	Isogeny class
Conductor	15210	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	314496	Modular degree for the optimal curve
Δ	-678367173765966750 = -1 · 2 · 39 · 53 · 1310	Discriminant
Eigenvalues	2+ 3- 5+ -2 -3 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1290600,-565400250]	[a1,a2,a3,a4,a6]
j	-2365581049/6750	j-invariant
L	0.14162091765269	L(r)(E,1)/r!
Ω	0.070810458826347	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	121680do1 5070u1 76050el1 15210bp1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 15210j1

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	-3	+	-6	-2	-3	-3	-5	7	6	-1	-3	6	-9	2	-8	-12	-14	5	-6	-18	-14

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Quadratic twists for elliptic curve 15210j1

-4	-3	5	13
121680do1	5070u1	76050el1	15210bp1

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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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