Properties

Label 381150s
Number of curves $2$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 381150s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.s2 381150s1 \([1, -1, 0, -5425602, -5345734124]\) \(-1787281834251393315/215504279044096\) \(-2129758750902111436800\) \([]\) \(23224320\) \(2.8278\) \(\Gamma_0(N)\)-optimal
381150.s1 381150s2 \([1, -1, 0, -451480002, -3692262895084]\) \(-1412658626195854329435/1927561216\) \(-13887057098402611200\) \([]\) \(69672960\) \(3.3771\)  

Rank

sage: E.rank()
 

The elliptic curves in class 381150s have rank \(0\).

Complex multiplication

The elliptic curves in class 381150s do not have complex multiplication.

Modular form 381150.2.a.s

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.