Cremona's table of elliptic curves

1360 = 2⁴ · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5- 17-	Signs for the Atkin-Lehner involutions
Class	1360c	Isogeny class
Conductor	1360	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	2720000 = 28 · 54 · 17	Discriminant
Eigenvalues	2+ -2 5- -2  2  2 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3540,79900]	[a1,a2,a3,a4,a6]
Generators	[30:40:1]	Generators of the group modulo torsion
j	19169739408976/10625	j-invariant
L	2.0504189115722	L(r)(E,1)/r!
Ω	2.0994772215487	Real period
R	0.48831654150068	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	680c1 5440s1 12240h1 6800c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1360c1

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	-	-2	2	2	-	-8	6	-2	-6	-2	-6	8	-8	6	0	-10	-12	-6	-14	-2	8	-10	2

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Quadratic twists for elliptic curve 1360c1

-4	8	-3	5	-7	17
680c1	5440s1	12240h1	6800c1	66640e1	23120d1

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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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