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	1	Product of Tamagawa factors cp
Δ	-5000 = -1 · 23 · 54	Discriminant
Eigenvalues	2+  1 5-  2 -3 -4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-126,-552]	[a1,a2,a3,a4,a6]
j	-349938025/8	j-invariant
L	0.7131649814283	L(r)(E,1)/r!
Ω	0.7131649814283	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	400c2 1600j2 450b2 50b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50a2

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 50a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
400c2	1600j2	450b2	50b4	2450p2	6050bi2	8450x2	14450l2	18050y2	26450i2	42050bh2	48050l2	68450bl2	84050f2	92450bh2	110450o2

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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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