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	13650cp	Isogeny class
Conductor	13650	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	111820800000000 = 220 · 3 · 58 · 7 · 13	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12088,-54208]	[a1,a2,a3,a4,a6]
j	12501706118329/7156531200	j-invariant
L	4.9362059963947	L(r)(E,1)/r!
Ω	0.49362059963947	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200dz1 40950bf1 2730d1 95550gs1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650cp1

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	-	-2	4	-4	2	-8	6	10	4	0	6	8	10	8	-16	-14	-16	-16	18	10

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Quadratic twists for elliptic curve 13650cp1

-4	-3	5	-7
109200dz1	40950bf1	2730d1	95550gs1

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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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