Cremona's table of elliptic curves

4305 = 3 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	3- 5- 7- 41-	Signs for the Atkin-Lehner involutions
Class	4305n	Isogeny class
Conductor	4305	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	14784	Modular degree for the optimal curve
Δ	-14956206774075 = -1 · 311 · 52 · 72 · 413	Discriminant
Eigenvalues	-2 3- 5- 7- -3  0 -1 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,3710,-163256]	[a1,a2,a3,a4,a6]
Generators	[161:-2153:1]	Generators of the group modulo torsion
j	5645837515526144/14956206774075	j-invariant
L	2.4485609166952	L(r)(E,1)/r!
Ω	0.36090918654073	Real period
R	0.051397150879296	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	68880bp1 12915j1 21525f1 30135h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4305n1

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	-	-	-	-3	0	-1	-2	2	1	-11	7	-	-11	-1	10	-14	7	-14	-3	-11	8	-10	-6	-12

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Quadratic twists for elliptic curve 4305n1

-4	-3	5	-7
68880bp1	12915j1	21525f1	30135h1

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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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