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	15210q	Isogeny class
Conductor	15210	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	134784	Modular degree for the optimal curve
Δ	61845440343336000 = 26 · 36 · 53 · 139	Discriminant
Eigenvalues	2+ 3- 5+  0  0 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-104220,4980496]	[a1,a2,a3,a4,a6]
Generators	[-145:4199:1]	Generators of the group modulo torsion
j	16194277/8000	j-invariant
L	3.0565206094445	L(r)(E,1)/r!
Ω	0.31065382597317	Real period
R	4.9194961624397	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	121680ef1 1690i1 76050ff1 15210bu1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 15210q1

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	0	-	-6	0	0	-6	-6	6	0	10	12	0	12	10	12	-6	-6	-8	12	12	-18

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Quadratic twists for elliptic curve 15210q1

-4	-3	5	13
121680ef1	1690i1	76050ff1	15210bu1

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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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