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	650c	Isogeny class
Conductor	650	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-8450 = -1 · 2 · 52 · 132	Discriminant
Eigenvalues	2+ -3 5+  0 -3 13+  7  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-22,46]	[a1,a2,a3,a4,a6]
Generators	[5:4:1]	Generators of the group modulo torsion
j	-48317985/338	j-invariant
L	1.082685142673	L(r)(E,1)/r!
Ω	4.1558626857111	Real period
R	0.13025997543128	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	5200u1 20800bg1 5850bk1 650m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650c1

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
+	-3	+	0	-3	+	7	1	4	4	-10	-12	-5	-12	4	-6	-4	4	5	0	11	4	-15	-11	2

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Quadratic twists for elliptic curve 650c1

-4	8	-3	5	-7	-11	13
5200u1	20800bg1	5850bk1	650m1	31850bf1	78650cs1	8450u1

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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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