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	318b	Isogeny class
Conductor	318	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-11448 = -1 · 23 · 33 · 53	Discriminant
Eigenvalues	2+ 3-  0  5 -3 -4  6  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-61,176]	[a1,a2,a3,a4,a6]
j	-24515367625/11448	j-invariant
L	1.3236964836554	L(r)(E,1)/r!
Ω	3.9710894509661	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2544c1 10176d1 954k1 7950bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 318b1

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	5	-3	-4	6	5	-3	3	8	-4	-3	-4	6	+	-12	-1	-13	-15	2	-16	0	0	5

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Quadratic twists for elliptic curve 318b1

-4	8	-3	5	-7	-11	13	17	-19	53
2544c1	10176d1	954k1	7950bi1	15582c1	38478i1	53742r1	91902a1	114798q1	16854l1

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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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