Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	2730m	Isogeny class
Conductor	2730	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	52587662400 = 26 · 34 · 52 · 74 · 132	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-939,-938]	[a1,a2,a3,a4,a6]
Generators	[-25:96:1]	Generators of the group modulo torsion
j	91422999252649/52587662400	j-invariant
L	2.8097710657865	L(r)(E,1)/r!
Ω	0.93813089221091	Real period
R	0.37438419962441	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840y2 87360bo2 8190br2 13650bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730m2

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	-8	-4	6	-8	-6	2	-12	0	10	-8	-2	-4	8	6	0	-4	-6	6

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Quadratic twists for elliptic curve 2730m2

-4	8	-3	5	-7	13
21840y2	87360bo2	8190br2	13650bv2	19110o2	35490dk2

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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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