Properties

Label 56550.w
Number of curves $1$
Conductor $56550$
CM no
Rank $1$

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

Elliptic curves in class 56550.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.w1 56550u1 \([1, 0, 1, 190299, 76492048]\) \(78043451459375/303887720448\) \(-2967653520000000000\) \([]\) \(861120\) \(2.2273\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 56550.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 56550.w do not have complex multiplication.

Modular form 56550.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 2 q^{11} + q^{12} - q^{13} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display