Cremona's table of elliptic curves

550 = 2 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	550f	Isogeny class
Conductor	550	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	-10065687500000 = -1 · 25 · 59 · 115	Discriminant
Eigenvalues	2+  1 5- -3 11- -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,4924,75298]	[a1,a2,a3,a4,a6]
Generators	[52:661:1]	Generators of the group modulo torsion
j	6761990971/5153632	j-invariant
L	1.6665638072801	L(r)(E,1)/r!
Ω	0.46396462077251	Real period
R	0.35920062277706	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	4400w2 17600w2 4950bq2 550k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550f2

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
+	1	-	-3	-	-4	-3	-5	-4	5	7	7	-8	6	-8	-9	0	-13	12	-3	6	0	-4	-15	12

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Quadratic twists for elliptic curve 550f2

-4	8	-3	5	-7	-11	13
4400w2	17600w2	4950bq2	550k2	26950bm2	6050bj2	92950cp2

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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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