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Properties

Label 145794.p
Number of curves $2$
Conductor $145794$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 145794.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145794.p1 145794s2 \([1, 0, 1, -38281, -301876]\) \(2808416463771625/1607794163712\) \(3551617307639808\) \([]\) \(746496\) \(1.6736\)  
145794.p2 145794s1 \([1, 0, 1, -27706, -1777300]\) \(1064699261301625/4105728\) \(9069553152\) \([]\) \(248832\) \(1.1243\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145794.p have rank \(0\).

Complex multiplication

The elliptic curves in class 145794.p do not have complex multiplication.

Modular form 145794.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + q^{13} + q^{14} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.