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	4	Product of Tamagawa factors cp
Δ	4062500 = 22 · 57 · 13	Discriminant
Eigenvalues	2+  0 5+  0  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34667,-2475759]	[a1,a2,a3,a4,a6]
Generators	[399:6663:1]	Generators of the group modulo torsion
j	294889639316481/260	j-invariant
L	1.615604580103	L(r)(E,1)/r!
Ω	0.34988063201696	Real period
R	4.6175879207417	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	5200n3 20800t3 5850bj3 130b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650a3

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 650a3

-4	8	-3	5	-7	-11	13
5200n3	20800t3	5850bj3	130b3	31850r4	78650cd4	8450m3

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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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