Properties

Label 1728.w
Number of curves $1$
Conductor $1728$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.w1 1728h1 \([0, 0, 0, 6, -2]\) \(1536\) \(-15552\) \([]\) \(96\) \(-0.50680\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.w1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.w

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