Properties

Label 314721.cw
Number of curves $1$
Conductor $314721$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 314721.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
314721.cw1 314721cw1 \([0, 0, 1, 1153977, 89914041]\) \(45056/27\) \(-101841855194960388387\) \([]\) \(15611904\) \(2.5285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 314721.cw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 314721.cw do not have complex multiplication.

Modular form 314721.2.a.cw

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