Cremona's table of elliptic curves

4290 = 2 · 3 · 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 11+ 13-	Signs for the Atkin-Lehner involutions
Class	4290r	Isogeny class
Conductor	4290	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-10617750000 = -1 · 24 · 33 · 56 · 112 · 13	Discriminant
Eigenvalues	2- 3+ 5+ -2 11+ 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1826,-31201]	[a1,a2,a3,a4,a6]
Generators	[71:415:1]	Generators of the group modulo torsion
j	-673350049820449/10617750000	j-invariant
L	4.1549089462495	L(r)(E,1)/r!
Ω	0.36482641561913	Real period
R	2.8471820901444	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	34320bz1 12870z1 21450u1 47190b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4290r1

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

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Quadratic twists for elliptic curve 4290r1

-4	-3	5	-11	13
34320bz1	12870z1	21450u1	47190b1	55770q1

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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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