Properties

Label 443760.w
Number of curves $1$
Conductor $443760$
CM no
Rank $1$

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

Elliptic curves in class 443760.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.w1 443760w1 \([0, -1, 0, -76425, 10143477]\) \(-30505984/9675\) \(-15656751999763200\) \([]\) \(3784704\) \(1.8205\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 443760.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 443760.w do not have complex multiplication.

Modular form 443760.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} + 5 q^{11} - 3 q^{13} - q^{15} + q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display