Cremona's table of elliptic curves

13650 = 2 · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	13650cm	Isogeny class
Conductor	13650	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	5706126562500 = 22 · 32 · 58 · 74 · 132	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12338,513792]	[a1,a2,a3,a4,a6]
Generators	[-32:952:1]	Generators of the group modulo torsion
j	13293525831769/365192100	j-invariant
L	8.1129182003364	L(r)(E,1)/r!
Ω	0.75694232824662	Real period
R	2.679503410494	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	109200dr2 40950x2 2730f2 95550hn2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650cm2

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
-	-	+	+	-4	+	2	4	-4	-6	4	2	-2	4	-8	-6	-12	-10	0	-8	-14	0	4	6	10

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Quadratic twists for elliptic curve 13650cm2

-4	-3	5	-7
109200dr2	40950x2	2730f2	95550hn2

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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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