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Properties

Label 141570.dx
Number of curves $2$
Conductor $141570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dx1")
 
E.isogeny_class()
 

Elliptic curves in class 141570.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.dx1 141570b2 \([1, -1, 1, -3124167872, 67472142589019]\) \(-21580315425730848803929/96405029296875000\) \(-15064984893877899169921875000\) \([3]\) \(205286400\) \(4.2590\)  
141570.dx2 141570b1 \([1, -1, 1, 92373313, 489450969461]\) \(557820238477845431/985142146218750\) \(-153945822737165041158468750\) \([]\) \(68428800\) \(3.7097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141570.dx have rank \(0\).

Complex multiplication

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

Modular form 141570.2.a.dx

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