Cremona's table of elliptic curves

1378 = 2 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2+ 13+ 53-	Signs for the Atkin-Lehner involutions
Class	1378a	Isogeny class
Conductor	1378	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3800	Modular degree for the optimal curve
Δ	-1225307193344 = -1 · 225 · 13 · 532	Discriminant
Eigenvalues	2+  1 -1  5  4 13+  5 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13809,625668]	[a1,a2,a3,a4,a6]
j	-291182446516741129/1225307193344	j-invariant
L	1.7353279796103	L(r)(E,1)/r!
Ω	0.86766398980517	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	11024h1 44096g1 12402h1 34450s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1378a1

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	5	4	+	5	-4	6	6	0	1	0	1	-11	-	14	-8	-8	-3	4	0	14	18	2

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Quadratic twists for elliptic curve 1378a1

-4	8	-3	5	-7	13	53
11024h1	44096g1	12402h1	34450s1	67522m1	17914i1	73034i1

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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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