Cremona's table of elliptic curves

5050 = 2 · 5² · 101

Field	Data	Notes
Atkin-Lehner	2+ 5+ 101+	Signs for the Atkin-Lehner involutions
Class	5050a	Isogeny class
Conductor	5050	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	-78906250000000 = -1 · 27 · 514 · 101	Discriminant
Eigenvalues	2+  0 5+  5  0  4  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,10708,-30384]	[a1,a2,a3,a4,a6]
Generators	[142:3179:8]	Generators of the group modulo torsion
j	8689723536879/5050000000	j-invariant
L	3.2438367004028	L(r)(E,1)/r!
Ω	0.36130312406397	Real period
R	4.4890792306414	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	40400m1 45450cg1 1010a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5050a1

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	+	5	0	4	3	-7	-6	-7	4	-8	-8	-11	-2	7	-12	-11	-6	-2	-4	2	-12	0	11

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Quadratic twists for elliptic curve 5050a1

-4	-3	5
40400m1	45450cg1	1010a1

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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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