Cremona's table of elliptic curves

Curve 85305q1

85305 = 3 · 5 · 112 · 47



Data for elliptic curve 85305q1

Field Data Notes
Atkin-Lehner 3- 5+ 11- 47+ Signs for the Atkin-Lehner involutions
Class 85305q Isogeny class
Conductor 85305 Conductor
∏ cp 6 Product of Tamagawa factors cp
deg 88128 Modular degree for the optimal curve
Δ -518227875 = -1 · 36 · 53 · 112 · 47 Discriminant
Eigenvalues  0 3- 5+  4 11-  1  0 -8 Hecke eigenvalues for primes up to 20
Equation [0,1,1,-10721,-430864] [a1,a2,a3,a4,a6]
Generators [280:4312:1] Generators of the group modulo torsion
j -1126379500601344/4282875 j-invariant
L 6.9162949751305 L(r)(E,1)/r!
Ω 0.23458879273491 Real period
R 4.9137719495977 Regulator
r 1 Rank of the group of rational points
S 0.99999999978973 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 85305r1 Quadratic twists by: -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
Back to Tables and computations