Cremona's table of elliptic curves

50 = 2 · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5-	Signs for the Atkin-Lehner involutions
Class	50a	Isogeny class
Conductor	50	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-1250 = -1 · 2 · 54	Discriminant
Eigenvalues	2+  1 5-  2 -3 -4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,-2]	[a1,a2,a3,a4,a6]
j	-25/2	j-invariant
L	0.7131649814283	L(r)(E,1)/r!
Ω	2.1394949442849	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	400c1 1600j1 450b1 50b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50a1

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	-	2	-3	-4	-3	5	6	0	2	2	-3	-4	12	6	0	2	-13	12	11	-10	-9	15	2

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Quadratic twists for elliptic curve 50a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
400c1	1600j1	450b1	50b3	2450p1	6050bi1	8450x1	14450l1	18050y1	26450i1	42050bh1	48050l1	68450bl1	84050f1	92450bh1	110450o1

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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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