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	4305h	Isogeny class
Conductor	4305	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	13843265625 = 32 · 56 · 74 · 41	Discriminant
Eigenvalues	-1 3- 5+ 7- -2 -4  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-18416,960375]	[a1,a2,a3,a4,a6]
Generators	[-47:1336:1]	Generators of the group modulo torsion
j	690734431140542209/13843265625	j-invariant
L	2.6132599178106	L(r)(E,1)/r!
Ω	1.1561617105579	Real period
R	0.56507231945727	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	68880bf1 12915s1 21525b1 30135r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4305h1

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
-1	-	+	-	-2	-4	4	-2	0	-2	4	10	+	-4	-12	4	8	2	-8	-6	-14	-10	-4	14	4

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Quadratic twists for elliptic curve 4305h1

-4	-3	5	-7
68880bf1	12915s1	21525b1	30135r1

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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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