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	54	Product of Tamagawa factors cp
deg	1800	Modular degree for the optimal curve
Δ	-1331200000000 = -1 · 218 · 58 · 13	Discriminant
Eigenvalues	2- -2 5-  5 -3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3263,-90983]	[a1,a2,a3,a4,a6]
j	-9836106385/3407872	j-invariant
L	1.8624927589619	L(r)(E,1)/r!
Ω	0.31041545982699	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	5200bj1 20800bn1 5850bb1 650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650l1

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 650l1

-4	8	-3	5	-7	-11	13
5200bj1	20800bn1	5850bb1	650b1	31850cj1	78650bf1	8450k1

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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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