Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1728.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.i1 1728p1 \([0, 0, 0, -108, -7344]\) \(-6\) \(-23219011584\) \([]\) \(1152\) \(0.66837\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.i1 has rank \(0\).

Complex multiplication

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

Modular form 1728.2.a.i

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