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	1378c	Isogeny class
Conductor	1378	Conductor
∏ cp	66	Product of Tamagawa factors cp
deg	1320	Modular degree for the optimal curve
Δ	-51528116224 = -1 · 211 · 132 · 533	Discriminant
Eigenvalues	2-  0 -1 -2  1 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7753,264905]	[a1,a2,a3,a4,a6]
Generators	[-31:704:1]	Generators of the group modulo torsion
j	-51532421181502689/51528116224	j-invariant
L	3.472328522473	L(r)(E,1)/r!
Ω	1.1187254375745	Real period
R	0.047027658844833	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	11024g1 44096f1 12402b1 34450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1378c1

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	-1	-2	1	+	3	-6	-1	2	-5	-12	-6	1	4	-	-1	-2	-2	-8	2	11	6	-9	17

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Quadratic twists for elliptic curve 1378c1

-4	8	-3	5	-7	13	53
11024g1	44096f1	12402b1	34450g1	67522u1	17914f1	73034a1

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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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