Cremona's table of elliptic curves

318 = 2 · 3 · 53

Field	Data	Notes
Atkin-Lehner	2- 3+ 53+	Signs for the Atkin-Lehner involutions
Class	318a	Isogeny class
Conductor	318	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	-25758 = -1 · 2 · 35 · 53	Discriminant
Eigenvalues	2- 3+  0  1  5  0  2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2,-7]	[a1,a2,a3,a4,a6]
j	857375/25758	j-invariant
L	1.8177609135852	L(r)(E,1)/r!
Ω	1.8177609135852	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	2544d1 10176i1 954d1 7950t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 318a1

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	5	0	2	-1	3	-1	-4	0	-9	0	6	+	-4	-7	1	7	-14	-8	8	-12	13

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Quadratic twists for elliptic curve 318a1

-4	8	-3	5	-7	-11	13	17	-19	53
2544d1	10176i1	954d1	7950t1	15582t1	38478a1	53742a1	91902x1	114798l1	16854d1

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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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