Cremona's table of elliptic curves

50 = 2 · 5²

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Class	50b	Isogeny class
Conductor	50	Conductor
∏ cp	15	Product of Tamagawa factors cp
Δ	-819200 = -1 · 215 · 52	Discriminant
Eigenvalues	2- -1 5+ -2 -3  4  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,22,-9]	[a1,a2,a3,a4,a6]
j	46969655/32768	j-invariant
L	0.95681122658763	L(r)(E,1)/r!
Ω	1.594685377646	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	400b2 1600c2 450d2 50a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50b2

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 50b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
400b2	1600c2	450d2	50a4	2450v2	6050g2	8450d2	14450t2	18050f2	26450o2	42050f2	48050v2	68450d2	84050j2	92450g2	110450bc2

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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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