Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.h1 1728r1 \([0, 0, 0, -6, -6]\) \(-13824\) \(-1728\) \([]\) \(96\) \(-0.62918\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.h1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.h

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