Cremona's table of elliptic curves

13650 = 2 · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	13650bt	Isogeny class
Conductor	13650	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	108000	Modular degree for the optimal curve
Δ	-5649199123276800 = -1 · 210 · 315 · 52 · 7 · 133	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -6 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6013,-3623149]	[a1,a2,a3,a4,a6]
j	-961749189765625/225967964931072	j-invariant
L	1.9089843091228	L(r)(E,1)/r!
Ω	0.19089843091228	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	109200gc1 40950y1 13650bp1 95550kf1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650bt1

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
-	+	+	+	-6	+	3	2	-3	6	2	10	0	-8	3	0	-9	-10	-5	-6	1	-4	-12	0	-11

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Quadratic twists for elliptic curve 13650bt1

-4	-3	5	-7
109200gc1	40950y1	13650bp1	95550kf1

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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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