Properties

Label 1728.u
Number of curves $1$
Conductor $1728$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.u1 1728z1 \([0, 0, 0, -54, -162]\) \(-13824\) \(-1259712\) \([]\) \(288\) \(-0.079872\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1728.u do not have complex multiplication.

Modular form 1728.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 3q^{7} - 6q^{11} + 3q^{13} + 2q^{17} - 3q^{19} + O(q^{20})\)  Toggle raw display