Cremona's table of elliptic curves

Curve 27360x1

27360 = 25 · 32 · 5 · 19



Data for elliptic curve 27360x1

Field Data Notes
Atkin-Lehner 2- 3- 5+ 19- Signs for the Atkin-Lehner involutions
Class 27360x Isogeny class
Conductor 27360 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 16384 Modular degree for the optimal curve
Δ 34106702400 = 26 · 310 · 52 · 192 Discriminant
Eigenvalues 2- 3- 5+  0 -4 -2 -2 19- Hecke eigenvalues for primes up to 20
Equation [0,0,0,-813,-812] [a1,a2,a3,a4,a6]
Generators [-16:90:1] [-3:40:1] Generators of the group modulo torsion
j 1273760704/731025 j-invariant
L 7.6452607533895 L(r)(E,1)/r!
Ω 0.97082887490451 Real period
R 3.9374914318154 Regulator
r 2 Rank of the group of rational points
S 0.99999999999979 (Analytic) order of Ш
t 4 Number of elements in the torsion subgroup
Twists 27360g1 54720bo2 9120j1 Quadratic twists by: -4 8 -3


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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