Properties

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

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

Elliptic curves in class 1728u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.b1 1728u1 \([0, 0, 0, -432, 4320]\) \(-3072\) \(-2902376448\) \([]\) \(1152\) \(0.52828\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728u1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.u

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + 3 q^{7} + 4 q^{11} - q^{13} - 4 q^{17} - q^{19} + O(q^{20})\)  Toggle raw display