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	650a	Isogeny class
Conductor	650	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1115664062500 = -1 · 22 · 510 · 134	Discriminant
Eigenvalues	2+  0 5+  0  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1667,-56759]	[a1,a2,a3,a4,a6]
Generators	[84:583:1]	Generators of the group modulo torsion
j	-32798729601/71402500	j-invariant
L	1.615604580103	L(r)(E,1)/r!
Ω	0.34988063201696	Real period
R	1.1543969801854	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5200n4 20800t4 5850bj4 130b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650a4

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
+	0	+	0	0	+	-2	-8	4	-2	-4	-6	10	0	-8	-6	8	-2	-4	-12	-10	-8	-12	10	14

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Quadratic twists for elliptic curve 650a4

-4	8	-3	5	-7	-11	13
5200n4	20800t4	5850bj4	130b4	31850r3	78650cd3	8450m4

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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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