Cremona's table of elliptic curves

Curve 42075bh1

42075 = 32 · 52 · 11 · 17



Data for elliptic curve 42075bh1

Field Data Notes
Atkin-Lehner 3- 5+ 11- 17+ Signs for the Atkin-Lehner involutions
Class 42075bh Isogeny class
Conductor 42075 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 432000 Modular degree for the optimal curve
Δ -384739716796875 = -1 · 36 · 510 · 11 · 173 Discriminant
Eigenvalues -2 3- 5+  0 11-  4 17+  2 Hecke eigenvalues for primes up to 20
Equation [0,0,1,-635625,195053906] [a1,a2,a3,a4,a6]
Generators [456:166:1] Generators of the group modulo torsion
j -3989321625600/54043 j-invariant
L 3.1120092995566 L(r)(E,1)/r!
Ω 0.48753767494531 Real period
R 3.1915577600296 Regulator
r 1 Rank of the group of rational points
S 0.9999999999999 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 4675j1 42075cm1 Quadratic twists by: -3 5


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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