Cremona's table of elliptic curves

650 = 2 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13-	Signs for the Atkin-Lehner involutions
Class	650l	Isogeny class
Conductor	650	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-54925000000 = -1 · 26 · 58 · 133	Discriminant
Eigenvalues	2- -2 5-  5 -3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-283263,-58050983]	[a1,a2,a3,a4,a6]
j	-6434774386429585/140608	j-invariant
L	1.8624927589619	L(r)(E,1)/r!
Ω	0.10347181994233	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	5200bj2 20800bn2 5850bb2 650b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650l2

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	-	5	-3	-	3	-4	6	9	5	2	0	2	-9	-9	-9	-1	5	0	14	-16	-15	-6	8

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Quadratic twists for elliptic curve 650l2

-4	8	-3	5	-7	-11	13
5200bj2	20800bn2	5850bb2	650b2	31850cj2	78650bf2	8450k2

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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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