Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 1728l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.a1 1728l1 \([0, 0, 0, -432, -4320]\) \(-3072\) \(-2902376448\) \([]\) \(1152\) \(0.52828\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728l1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.l

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