Cremona's table of elliptic curves

10050 = 2 · 3 · 5² · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 67+	Signs for the Atkin-Lehner involutions
Class	10050bf	Isogeny class
Conductor	10050	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-2713500000000 = -1 · 28 · 34 · 59 · 67	Discriminant
Eigenvalues	2- 3- 5+  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3162,-39708]	[a1,a2,a3,a4,a6]
Generators	[36:330:1]	Generators of the group modulo torsion
j	223759095911/173664000	j-invariant
L	8.0045449766718	L(r)(E,1)/r!
Ω	0.45021878730789	Real period
R	2.2224041961175	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	80400bz1 30150q1 2010a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 10050bf1

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

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Quadratic twists for elliptic curve 10050bf1

-4	-3	5
80400bz1	30150q1	2010a1

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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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