Properties

Label 457776w
Number of curves $1$
Conductor $457776$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 457776w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.w1 457776w1 \([0, 0, 0, -155199936, -744193963024]\) \(-5736108018368512/11042163\) \(-795857215871195394048\) \([]\) \(53084160\) \(3.2643\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457776w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457776w do not have complex multiplication.

Modular form 457776.2.a.w

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