Cremona's table of elliptic curves

17424 = 2⁴ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	17424bf	Isogeny class
Conductor	17424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	88704	Modular degree for the optimal curve
Δ	-2868471661473792 = -1 · 212 · 33 · 1110	Discriminant
Eigenvalues	2- 3+  0  5 11- -2  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,2576816]	[a1,a2,a3,a4,a6]
Generators	[-12355:158667:125]	Generators of the group modulo torsion
j	0	j-invariant
L	5.823744926253	L(r)(E,1)/r!
Ω	0.35926240565764	Real period
R	8.1051410258088	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	1089b1 69696ej1 17424bf2 17424bg1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bf1

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	5	-	-2	0	-7	0	0	-11	11	0	8	0	0	0	1	-11	0	-17	-13	0	0	5

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Quadratic twists for elliptic curve 17424bf1

-4	8	-3	-11
1089b1	69696ej1	17424bf2	17424bg1

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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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