Cremona's table of elliptic curves

Curve 8670c1

8670 = 2 · 3 · 5 · 172



Data for elliptic curve 8670c1

Field Data Notes
Atkin-Lehner 2+ 3+ 5+ 17+ Signs for the Atkin-Lehner involutions
Class 8670c Isogeny class
Conductor 8670 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 96768 Modular degree for the optimal curve
Δ -15429259338301440 = -1 · 214 · 33 · 5 · 178 Discriminant
Eigenvalues 2+ 3+ 5+  2 -4  0 17+  4 Hecke eigenvalues for primes up to 20
Equation [1,1,0,-208808,-37295808] [a1,a2,a3,a4,a6]
Generators [216198167:9499343655:103823] Generators of the group modulo torsion
j -41713327443241/639221760 j-invariant
L 2.5016689210321 L(r)(E,1)/r!
Ω 0.11156732254074 Real period
R 11.211476909463 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 69360dd1 26010bu1 43350db1 510b1 Quadratic twists by: -4 -3 5 17


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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