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	15210b	Isogeny class
Conductor	15210	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	87360	Modular degree for the optimal curve
Δ	-8809891786800000 = -1 · 27 · 33 · 55 · 138	Discriminant
Eigenvalues	2+ 3+ 5+  0  3 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-71265,8620925]	[a1,a2,a3,a4,a6]
Generators	[127:1204:1]	Generators of the group modulo torsion
j	-1817378667/400000	j-invariant
L	3.4136060544984	L(r)(E,1)/r!
Ω	0.39374384161323	Real period
R	1.4449352149494	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	121680ce1 15210bd1 76050de1 15210be1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 15210b1

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	3	+	-2	-2	1	5	5	-3	2	-9	7	-12	1	-8	4	-6	4	1	-6	8	-14

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Quadratic twists for elliptic curve 15210b1

-4	-3	5	13
121680ce1	15210bd1	76050de1	15210be1

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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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