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	13650dh	Isogeny class
Conductor	13650	Conductor
∏ cp	270	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-49533120000 = -1 · 29 · 35 · 54 · 72 · 13	Discriminant
Eigenvalues	2- 3- 5- 7- -6 13+ -4  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,162,10692]	[a1,a2,a3,a4,a6]
Generators	[72:-666:1]	Generators of the group modulo torsion
j	752005775/79252992	j-invariant
L	8.4023091045332	L(r)(E,1)/r!
Ω	0.86540735026993	Real period
R	0.035959555162568	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	109200ek1 40950cn1 13650g1 95550iq1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650dh1

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

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Quadratic twists for elliptic curve 13650dh1

-4	-3	5	-7
109200ek1	40950cn1	13650g1	95550iq1

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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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