Properties

Label 1728y
Number of curves $1$
Conductor $1728$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 1728y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.k1 1728y1 \([0, 0, 0, -108, 1296]\) \(-216\) \(-644972544\) \([]\) \(576\) \(0.37510\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728y1 has rank \(1\).

Complex multiplication

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

Modular form 1728.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{5} + 3 q^{7} - 3 q^{11} - 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display