Cremona's table of elliptic curves

Curve 42944r1

42944 = 26 · 11 · 61



Data for elliptic curve 42944r1

Field Data Notes
Atkin-Lehner 2- 11+ 61- Signs for the Atkin-Lehner involutions
Class 42944r Isogeny class
Conductor 42944 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 27648 Modular degree for the optimal curve
Δ 42567467008 = 219 · 113 · 61 Discriminant
Eigenvalues 2-  1  2 -4 11+  3 -3  0 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-2337,41567] [a1,a2,a3,a4,a6]
Generators [7:160:1] Generators of the group modulo torsion
j 5386984777/162382 j-invariant
L 6.5539505944296 L(r)(E,1)/r!
Ω 1.137147920914 Real period
R 1.4408746817118 Regulator
r 1 Rank of the group of rational points
S 1.0000000000007 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 42944k1 10736h1 Quadratic twists by: -4 8


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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