Cremona's table of elliptic curves

13780 = 2² · 5 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2- 5- 13+ 53-	Signs for the Atkin-Lehner involutions
Class	13780b	Isogeny class
Conductor	13780	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	81792	Modular degree for the optimal curve
Δ	173353867570000 = 24 · 54 · 133 · 534	Discriminant
Eigenvalues	2-  0 5- -2  6 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-456772,-118820439]	[a1,a2,a3,a4,a6]
j	658721974179766910976/10834616723125	j-invariant
L	2.2037197346072	L(r)(E,1)/r!
Ω	0.18364331121726	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55120o1 124020f1 68900e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13780b1

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
-	0	-	-2	6	+	6	-2	0	2	-2	10	-2	-4	6	-	6	-2	-10	6	-2	4	-10	2	-6

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Quadratic twists for elliptic curve 13780b1

-4	-3	5
55120o1	124020f1	68900e1

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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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