Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.t1 1728n1 \([0, 0, 0, -12, -48]\) \(-216\) \(-884736\) \([]\) \(192\) \(-0.17420\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.t1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.t

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