Properties

Label 301665.w
Number of curves $1$
Conductor $301665$
CM no
Rank $1$

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

Elliptic curves in class 301665.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.w1 301665w1 \([0, -1, 1, -5971, 264552]\) \(-4878401536/3346875\) \(-16154726371875\) \([]\) \(538560\) \(1.2348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 301665.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 301665.w do not have complex multiplication.

Modular form 301665.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} + q^{7} + q^{9} + 2 q^{11} + 2 q^{12} + q^{15} + 4 q^{16} + q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display