Cremona's table of elliptic curves

1550 = 2 · 5² · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 31-	Signs for the Atkin-Lehner involutions
Class	1550d	Isogeny class
Conductor	1550	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	6933622507812500 = 22 · 59 · 316	Discriminant
Eigenvalues	2+  2 5+  4  0  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-51150,1922000]	[a1,a2,a3,a4,a6]
j	947226559343329/443751840500	j-invariant
L	2.2527379979944	L(r)(E,1)/r!
Ω	0.37545633299907	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	12400q4 49600ba4 13950cq4 310b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1550d4

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
+	2	+	4	0	4	0	-4	6	6	-	-8	-6	10	0	0	-12	14	-8	0	4	8	-6	-18	10

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Quadratic twists for elliptic curve 1550d4

-4	8	-3	5	-7	-31
12400q4	49600ba4	13950cq4	310b4	75950o4	48050e4

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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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