Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.f1 1728d1 \([0, 0, 0, 54, -54]\) \(1536\) \(-11337408\) \([]\) \(288\) \(0.042505\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.f1 has rank \(1\).

Complex multiplication

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

Modular form 1728.2.a.f

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