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Properties

Label 141570.t
Number of curves $2$
Conductor $141570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 141570.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.t1 141570ec2 \([1, -1, 0, -18140040, -29733462720]\) \(-511157582445795481/8504770560\) \(-10983638761934192640\) \([]\) \(6220800\) \(2.7845\)  
141570.t2 141570ec1 \([1, -1, 0, -89865, -88917075]\) \(-62146192681/2610036000\) \(-3370777891936884000\) \([]\) \(2073600\) \(2.2352\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141570.t have rank \(1\).

Complex multiplication

The elliptic curves in class 141570.t do not have complex multiplication.

Modular form 141570.2.a.t

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