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	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	117411840 = 212 · 32 · 5 · 72 · 13	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-619,5846]	[a1,a2,a3,a4,a6]
Generators	[16:2:1]	Generators of the group modulo torsion
j	26168974809769/117411840	j-invariant
L	2.8097710657865	L(r)(E,1)/r!
Ω	1.8762617844218	Real period
R	0.74876839924882	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	21840y1 87360bo1 8190br1 13650bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730m1

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 2730m1

-4	8	-3	5	-7	13
21840y1	87360bo1	8190br1	13650bv1	19110o1	35490dk1

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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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