Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 177870.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.h1 177870ij1 \([1, 1, 0, -87787438, 349990856692]\) \(-861923363555648023441/110929177533556800\) \(-9629372429345745490075200\) \([]\) \(49420800\) \(3.5274\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177870.h1 has rank \(1\).

Complex multiplication

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

Modular form 177870.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} - 4 q^{13} + q^{15} + q^{16} + 7 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display