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	13650dg	Isogeny class
Conductor	13650	Conductor
∏ cp	1512	Product of Tamagawa factors cp
Δ	468175984540992000 = 29 · 314 · 53 · 76 · 13	Discriminant
Eigenvalues	2- 3- 5- 7- -4 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-255633,-37318743]	[a1,a2,a3,a4,a6]
Generators	[-294:3675:1]	Generators of the group modulo torsion
j	14779663816445754533/3745407876327936	j-invariant
L	8.3983083587708	L(r)(E,1)/r!
Ω	0.21628248586926	Real period
R	0.10272559468502	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	109200ej2 40950cm2 13650q2 95550im2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650dg2

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	+	-4	-4	0	4	2	0	-6	4	4	-10	4	4	2	-10	-10	-8	-6	-6	18

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Quadratic twists for elliptic curve 13650dg2

-4	-3	5	-7
109200ej2	40950cm2	13650q2	95550im2

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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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