Cremona's table of elliptic curves

Curve 85211b1

85211 = 72 · 37 · 47



Data for elliptic curve 85211b1

Field Data Notes
Atkin-Lehner 7+ 37+ 47- Signs for the Atkin-Lehner involutions
Class 85211b Isogeny class
Conductor 85211 Conductor
∏ cp 1 Product of Tamagawa factors cp
deg 394464 Modular degree for the optimal curve
Δ -10024988939 = -1 · 78 · 37 · 47 Discriminant
Eigenvalues  1  3  3 7+  0 -5  2  5 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-67678,6793667] [a1,a2,a3,a4,a6]
j -5946830358777/1739 j-invariant
L 9.3076535262727 L(r)(E,1)/r!
Ω 1.0341837281031 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 9 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 85211d1 Quadratic twists by: -7


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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