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
deg	96768	Modular degree for the optimal curve
Δ	4154124828672000 = 218 · 37 · 53 · 73 · 132	Discriminant
Eigenvalues	2- 3- 5- 7- -4 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-89233,9772457]	[a1,a2,a3,a4,a6]
Generators	[-214:4475:1]	Generators of the group modulo torsion
j	628623316769266853/33232998629376	j-invariant
L	8.3983083587708	L(r)(E,1)/r!
Ω	0.43256497173853	Real period
R	0.051362797342511	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	109200ej1 40950cm1 13650q1 95550im1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650dg1

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 13650dg1

-4	-3	5	-7
109200ej1	40950cm1	13650q1	95550im1

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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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