Properties

Label 177870.w
Number of curves $1$
Conductor $177870$
CM no
Rank $0$

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

Elliptic curves in class 177870.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.w1 177870je1 \([1, 1, 0, 1778577, -909128667]\) \(4161311/4800\) \(-717715638130893124800\) \([]\) \(10378368\) \(2.6882\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177870.w1 has rank \(0\).

Complex multiplication

The elliptic curves in class 177870.w do not have complex multiplication.

Modular form 177870.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} + 3 q^{13} + q^{15} + q^{16} - q^{18} + O(q^{20})\) Copy content Toggle raw display