Properties

Label 177744.t
Number of curves $1$
Conductor $177744$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 177744.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.t1 177744db1 \([0, -1, 0, -245233996, 135723144112]\) \(153796840255696/88253338509\) \(935943146850572702235991296\) \([]\) \(57867264\) \(3.8650\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177744.t do not have complex multiplication.

Modular form 177744.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - 2 q^{13} + q^{15} - q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display