Cremona's table of elliptic curves

1364 = 2² · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 11+ 31-	Signs for the Atkin-Lehner involutions
Class	1364a	Isogeny class
Conductor	1364	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-60016 = -1 · 24 · 112 · 31	Discriminant
Eigenvalues	2- -2  1  1 11+  0 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10,1]	[a1,a2,a3,a4,a6]
Generators	[4:11:1]	Generators of the group modulo torsion
j	6243584/3751	j-invariant
L	2.1386811865336	L(r)(E,1)/r!
Ω	2.0440725994215	Real period
R	0.17438072626341	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	5456i1 21824n1 12276e1 34100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1364a1

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
-	-2	1	1	+	0	-6	1	4	0	-	-4	-3	-4	8	2	-3	-12	-8	-3	-6	-4	-12	-8	-3

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Quadratic twists for elliptic curve 1364a1

-4	8	-3	5	-7	-11	-31
5456i1	21824n1	12276e1	34100b1	66836b1	15004c1	42284f1

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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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