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	1056250000 = 24 · 58 · 132	Discriminant
Eigenvalues	2+  0 5+  0  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2167,-38259]	[a1,a2,a3,a4,a6]
Generators	[-27:18:1]	Generators of the group modulo torsion
j	72043225281/67600	j-invariant
L	1.615604580103	L(r)(E,1)/r!
Ω	0.69976126403393	Real period
R	2.3087939603708	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5200n2 20800t2 5850bj2 130b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650a2

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 650a2

-4	8	-3	5	-7	-11	13
5200n2	20800t2	5850bj2	130b2	31850r2	78650cd2	8450m2

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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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