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	650g	Isogeny class
Conductor	650	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-87880000 = -1 · 26 · 54 · 133	Discriminant
Eigenvalues	2+ -2 5- -1  3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,99,248]	[a1,a2,a3,a4,a6]
Generators	[11:-58:1]	Generators of the group modulo torsion
j	174196775/140608	j-invariant
L	1.2442250386561	L(r)(E,1)/r!
Ω	1.2333181666217	Real period
R	0.16814058641823	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200bi2 20800bm2 5850ca2 650i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650g2

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	-	-1	3	-	3	-4	-6	-3	-1	2	0	-10	-3	3	-15	-13	-13	0	-10	-4	15	6	-4

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Quadratic twists for elliptic curve 650g2

-4	8	-3	5	-7	-11	13
5200bi2	20800bm2	5850ca2	650i2	31850bk2	78650df2	8450y2

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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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