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	650h	Isogeny class
Conductor	650	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-406250 = -1 · 2 · 56 · 13	Discriminant
Eigenvalues	2- -1 5+  1  6 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,12,31]	[a1,a2,a3,a4,a6]
j	12167/26	j-invariant
L	2.0751559917619	L(r)(E,1)/r!
Ω	2.0751559917619	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200p1 20800v1 5850i1 26a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650h1

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
-	-1	+	1	6	+	3	2	0	6	-4	7	0	1	-3	0	-6	8	-14	-3	-2	8	-12	-6	10

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Quadratic twists for elliptic curve 650h1

-4	8	-3	5	-7	-11	13
5200p1	20800v1	5850i1	26a3	31850bz1	78650p1	8450c1

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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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