Cremona's table of elliptic curves

330 = 2 · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11-	Signs for the Atkin-Lehner involutions
Class	330a	Isogeny class
Conductor	330	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	1069200 = 24 · 35 · 52 · 11	Discriminant
Eigenvalues	2+ 3+ 5+  0 11-  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1393,-20603]	[a1,a2,a3,a4,a6]
j	299270638153369/1069200	j-invariant
L	0.78139617558096	L(r)(E,1)/r!
Ω	0.78139617558096	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2640r1 10560z1 990k1 1650q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 330a1

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	-	2	-2	8	4	2	8	-2	6	8	-4	2	4	-6	-12	-12	2	0	4	-6	-14

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Quadratic twists for elliptic curve 330a1

-4	8	-3	5	-7	-11	13	17	-19
2640r1	10560z1	990k1	1650q1	16170bd1	3630n1	55770cc1	95370bh1	119130bo1

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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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