Cremona's table of elliptic curves

Curve 27450bg1

27450 = 2 · 32 · 52 · 61



Data for elliptic curve 27450bg1

Field Data Notes
Atkin-Lehner 2- 3+ 5+ 61- Signs for the Atkin-Lehner involutions
Class 27450bg Isogeny class
Conductor 27450 Conductor
∏ cp 22 Product of Tamagawa factors cp
deg 57024 Modular degree for the optimal curve
Δ -38421216000000 = -1 · 211 · 39 · 56 · 61 Discriminant
Eigenvalues 2- 3+ 5+  0  2  2 -1  2 Hecke eigenvalues for primes up to 20
Equation [1,-1,1,7045,-194453] [a1,a2,a3,a4,a6]
Generators [43:410:1] Generators of the group modulo torsion
j 125751501/124928 j-invariant
L 8.8236861196034 L(r)(E,1)/r!
Ω 0.3526537477397 Real period
R 1.137310022567 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 27450d1 1098b1 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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