Cremona's table of elliptic curves

13350 = 2 · 3 · 5² · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 89+	Signs for the Atkin-Lehner involutions
Class	13350p	Isogeny class
Conductor	13350	Conductor
∏ cp	250	Product of Tamagawa factors cp
deg	96000	Modular degree for the optimal curve
Δ	-4408516332748800 = -1 · 225 · 310 · 52 · 89	Discriminant
Eigenvalues	2- 3- 5+  3 -3 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,21722,2949092]	[a1,a2,a3,a4,a6]
Generators	[116:2594:1]	Generators of the group modulo torsion
j	45340038226926455/176340653309952	j-invariant
L	8.7655570437719	L(r)(E,1)/r!
Ω	0.31087224332448	Real period
R	2.8196653873092	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	106800bc1 40050o1 13350d2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13350p1

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
-	-	+	3	-3	-6	-2	0	-1	5	-8	-7	-8	4	-2	-6	0	-3	-7	12	9	10	-6	+	-7

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Quadratic twists for elliptic curve 13350p1

-4	-3	5
106800bc1	40050o1	13350d2

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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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