Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1728.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.s1 1728b1 \([0, 0, 0, -12, -272]\) \(-6\) \(-31850496\) \([]\) \(384\) \(0.11906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.s1 has rank \(1\).

Complex multiplication

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

Modular form 1728.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{5} + 3 q^{7} - 5 q^{11} - 4 q^{13} - 8 q^{17} - 2 q^{19} + O(q^{20})\)  Toggle raw display