Properties

Label 252050.w
Number of curves $1$
Conductor $252050$
CM no
Rank $1$

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

Elliptic curves in class 252050.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
252050.w1 252050w1 \([1, -1, 1, -330965280, -2307882574653]\) \(2003092024307193/9529458688\) \(19073849430410002432000000\) \([]\) \(209018880\) \(3.7001\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 252050.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 252050.w do not have complex multiplication.

Modular form 252050.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 3 q^{6} - 3 q^{7} + q^{8} + 6 q^{9} + 6 q^{11} - 3 q^{12} - 5 q^{13} - 3 q^{14} + q^{16} + 6 q^{17} + 6 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display