Cremona's table of elliptic curves

Curve 41745r1

41745 = 3 · 5 · 112 · 23



Data for elliptic curve 41745r1

Field Data Notes
Atkin-Lehner 3+ 5- 11- 23- Signs for the Atkin-Lehner involutions
Class 41745r Isogeny class
Conductor 41745 Conductor
∏ cp 18 Product of Tamagawa factors cp
deg 89856 Modular degree for the optimal curve
Δ -440279296875 = -1 · 34 · 59 · 112 · 23 Discriminant
Eigenvalues -2 3+ 5- -4 11- -2 -3 -2 Hecke eigenvalues for primes up to 20
Equation [0,-1,1,-4440,119756] [a1,a2,a3,a4,a6]
Generators [-70:287:1] [30:-113:1] Generators of the group modulo torsion
j -80017515483136/3638671875 j-invariant
L 3.8563064866238 L(r)(E,1)/r!
Ω 0.93125735216985 Real period
R 0.2300537534095 Regulator
r 2 Rank of the group of rational points
S 1.0000000000001 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 125235n1 41745q1 Quadratic twists by: -3 -11


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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