Cremona's table of elliptic curves

3318 = 2 · 3 · 7 · 79

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 79-	Signs for the Atkin-Lehner involutions
Class	3318d	Isogeny class
Conductor	3318	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	232206912 = 26 · 38 · 7 · 79	Discriminant
Eigenvalues	2+ 3- -4 7+  0  4 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-228,-1118]	[a1,a2,a3,a4,a6]
Generators	[-10:18:1]	Generators of the group modulo torsion
j	1302528459961/232206912	j-invariant
L	2.3547182520197	L(r)(E,1)/r!
Ω	1.2443022903307	Real period
R	0.47310012010703	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	26544m1 106176f1 9954f1 82950bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3318d1

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
+	-	-4	+	0	4	-6	6	0	0	-4	4	-10	-6	8	4	12	2	-16	-16	2	-	18	18	-18

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Quadratic twists for elliptic curve 3318d1

-4	8	-3	5	-7
26544m1	106176f1	9954f1	82950bz1	23226i1

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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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