Cremona's table of elliptic curves

Curve 12648f2

12648 = 23 · 3 · 17 · 31



Data for elliptic curve 12648f2

Field Data Notes
Atkin-Lehner 2- 3- 17+ 31+ Signs for the Atkin-Lehner involutions
Class 12648f Isogeny class
Conductor 12648 Conductor
∏ cp 288 Product of Tamagawa factors cp
Δ 2.3005912633924E+21 Discriminant
Eigenvalues 2- 3-  2  0 -4 -2 17+  4 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-128937092,563479546080] [a1,a2,a3,a4,a6]
Generators [-962:828630:1] Generators of the group modulo torsion
j 926013596462780608574574928/8986684622626442601 j-invariant
L 6.2005897024512 L(r)(E,1)/r!
Ω 0.13156400960398 Real period
R 2.618324013753 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 4 Number of elements in the torsion subgroup
Twists 25296a2 101184b2 37944f2 Quadratic twists by: -4 8 -3


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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