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	1378d	Isogeny class
Conductor	1378	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	648	Modular degree for the optimal curve
Δ	-3159742976 = -1 · 29 · 133 · 532	Discriminant
Eigenvalues	2-  1 -3 -1  0 13- -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-52,2704]	[a1,a2,a3,a4,a6]
Generators	[-6:56:1]	Generators of the group modulo torsion
j	-15568817473/3159742976	j-invariant
L	3.7125723361875	L(r)(E,1)/r!
Ω	1.1578811685524	Real period
R	0.53439167406518	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	11024i1 44096d1 12402f1 34450e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1378d1

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	-3	-1	0	-	-3	-4	-6	-6	8	-1	0	5	-9	+	-6	8	-4	3	-4	-4	6	6	2

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Quadratic twists for elliptic curve 1378d1

-4	8	-3	5	-7	13	53
11024i1	44096d1	12402f1	34450e1	67522o1	17914b1	73034e1

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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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