Cremona's table of elliptic curves

4214 = 2 · 7² · 43

Field	Data	Notes
Atkin-Lehner	2+ 7- 43-	Signs for the Atkin-Lehner involutions
Class	4214c	Isogeny class
Conductor	4214	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-70824698 = -1 · 2 · 77 · 43	Discriminant
Eigenvalues	2+ -3 -2 7- -3 -2  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-58,454]	[a1,a2,a3,a4,a6]
Generators	[9:20:1]	Generators of the group modulo torsion
j	-185193/602	j-invariant
L	1.1614180093419	L(r)(E,1)/r!
Ω	1.7087616970228	Real period
R	0.16992100352047	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33712n1 37926bw1 105350cl1 602c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4214c1

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
+	-3	-2	-	-3	-2	0	-1	6	-1	-5	-7	8	-	12	-6	-12	6	15	-5	2	4	12	7	-12

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Quadratic twists for elliptic curve 4214c1

-4	-3	5	-7
33712n1	37926bw1	105350cl1	602c1

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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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