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	650b	Isogeny class
Conductor	650	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-85196800 = -1 · 218 · 52 · 13	Discriminant
Eigenvalues	2+  2 5+ -5 -3 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-130,-780]	[a1,a2,a3,a4,a6]
Generators	[84:726:1]	Generators of the group modulo torsion
j	-9836106385/3407872	j-invariant
L	1.9367249329638	L(r)(E,1)/r!
Ω	0.69411006944	Real period
R	1.395113698989	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	5200t1 20800bf1 5850bo1 650l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650b1

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	+	-5	-3	+	-3	-4	-6	9	5	-2	0	-2	9	9	-9	-1	-5	0	-14	-16	15	-6	-8

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Quadratic twists for elliptic curve 650b1

-4	8	-3	5	-7	-11	13
5200t1	20800bf1	5850bo1	650l1	31850be1	78650cn1	8450r1

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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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