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
deg	72	Modular degree for the optimal curve
Δ	-32500 = -1 · 22 · 54 · 13	Discriminant
Eigenvalues	2+ -2 5- -1  3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-26,48]	[a1,a2,a3,a4,a6]
Generators	[-3:11:1]	Generators of the group modulo torsion
j	-2941225/52	j-invariant
L	1.2442250386561	L(r)(E,1)/r!
Ω	3.699954499865	Real period
R	0.50442175925469	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5200bi1 20800bm1 5850ca1 650i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650g1

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 650g1

-4	8	-3	5	-7	-11	13
5200bi1	20800bm1	5850ca1	650i1	31850bk1	78650df1	8450y1

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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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