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	13650df	Isogeny class
Conductor	13650	Conductor
∏ cp	840	Product of Tamagawa factors cp
deg	268800	Modular degree for the optimal curve
Δ	-2048738215387500000 = -1 · 25 · 37 · 58 · 78 · 13	Discriminant
Eigenvalues	2- 3- 5- 7-  0 13+ -4 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-395513,117901017]	[a1,a2,a3,a4,a6]
Generators	[352:4549:1]	Generators of the group modulo torsion
j	-17516447604815665/5244769831392	j-invariant
L	8.6408933485856	L(r)(E,1)/r!
Ω	0.24775862707272	Real period
R	0.041519352595202	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	109200eh1 40950cj1 13650d1 95550ie1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650df1

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
-	-	-	-	0	+	-4	-5	-8	-5	4	-5	9	6	-1	1	-2	-8	-5	-5	-4	15	-6	2	-4

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Quadratic twists for elliptic curve 13650df1

-4	-3	5	-7
109200eh1	40950cj1	13650d1	95550ie1

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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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