Cremona's table of elliptic curves

Curve 17850a1

17850 = 2 · 3 · 52 · 7 · 17



Data for elliptic curve 17850a1

Field Data Notes
Atkin-Lehner 2+ 3+ 5+ 7+ 17+ Signs for the Atkin-Lehner involutions
Class 17850a Isogeny class
Conductor 17850 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 430080 Modular degree for the optimal curve
Δ -4245034106880000000 = -1 · 228 · 35 · 57 · 72 · 17 Discriminant
Eigenvalues 2+ 3+ 5+ 7+ -4  6 17+ -4 Hecke eigenvalues for primes up to 20
Equation [1,1,0,390600,31752000] [a1,a2,a3,a4,a6]
Generators [31240:3809555:512] Generators of the group modulo torsion
j 421792317902132351/271682182840320 j-invariant
L 2.7933956612919 L(r)(E,1)/r!
Ω 0.1535565169851 Real period
R 9.0956597484007 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 53550ds1 3570x1 124950df1 Quadratic twists by: -3 5 -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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