Cremona's table of elliptic curves

4216 = 2³ · 17 · 31

Field	Data	Notes
Atkin-Lehner	2+ 17- 31-	Signs for the Atkin-Lehner involutions
Class	4216c	Isogeny class
Conductor	4216	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-143344 = -1 · 24 · 172 · 31	Discriminant
Eigenvalues	2+  0  3 -1  0 -4 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11,23]	[a1,a2,a3,a4,a6]
Generators	[7:17:1]	Generators of the group modulo torsion
j	-9199872/8959	j-invariant
L	4.0220378019847	L(r)(E,1)/r!
Ω	2.9757524397484	Real period
R	0.33790090770494	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	8432d1 33728h1 37944k1 105400n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4216c1

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	3	-1	0	-4	-	-3	0	6	-	-2	5	2	-8	6	-5	-8	-8	-15	-16	0	-4	12	-9

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Quadratic twists for elliptic curve 4216c1

-4	8	-3	5	17
8432d1	33728h1	37944k1	105400n1	71672a1

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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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