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	13650ck	Isogeny class
Conductor	13650	Conductor
∏ cp	1760	Product of Tamagawa factors cp
deg	506880	Modular degree for the optimal curve
Δ	1.232542531584E+19	Discriminant
Eigenvalues	2- 3- 5+ 7+  2 13+ -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1879588,977195792]	[a1,a2,a3,a4,a6]
Generators	[3272:-174436:1]	Generators of the group modulo torsion
j	46999332667159819129/788827220213760	j-invariant
L	8.3606833725766	L(r)(E,1)/r!
Ω	0.22560372588276	Real period
R	0.084225351532388	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	109200dp1 40950s1 2730e1 95550hf1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650ck1

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

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Quadratic twists for elliptic curve 13650ck1

-4	-3	5	-7
109200dp1	40950s1	2730e1	95550hf1

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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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