Cremona's table of elliptic curves

Curve 4176a1

4176 = 24 · 32 · 29



Data for elliptic curve 4176a1

Field Data Notes
Atkin-Lehner 2+ 3+ 29+ Signs for the Atkin-Lehner involutions
Class 4176a Isogeny class
Conductor 4176 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 768 Modular degree for the optimal curve
Δ -9132912 = -1 · 24 · 39 · 29 Discriminant
Eigenvalues 2+ 3+  0  1 -3  1 -7  6 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-135,621] [a1,a2,a3,a4,a6]
Generators [12:27:1] Generators of the group modulo torsion
j -864000/29 j-invariant
L 3.6885493971644 L(r)(E,1)/r!
Ω 2.2973768936393 Real period
R 0.80277411324561 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 2088a1 16704bu1 4176c1 104400a1 Quadratic twists by: -4 8 -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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