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	650d	Isogeny class
Conductor	650	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	840	Modular degree for the optimal curve
Δ	-211250000000 = -1 · 27 · 510 · 132	Discriminant
Eigenvalues	2+  1 5+  4  1 13-  7 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,299,22048]	[a1,a2,a3,a4,a6]
j	304175/21632	j-invariant
L	1.5261789914648	L(r)(E,1)/r!
Ω	0.7630894957324	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	5200y1 20800k1 5850bs1 650k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650d1

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	+	4	1	-	7	-3	0	-4	6	8	-5	4	-12	10	4	8	9	-8	-13	8	-3	-11	10

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Quadratic twists for elliptic curve 650d1

-4	8	-3	5	-7	-11	13
5200y1	20800k1	5850bs1	650k1	31850k1	78650bv1	8450p1

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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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