Properties

Label 324870.dt
Number of curves $2$
Conductor $324870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dt1")
 
E.isogeny_class()
 

Elliptic curves in class 324870.dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.dt1 324870dt1 \([1, 1, 1, -32215051, -70391328967]\) \(31427652507069423952801/654426190080\) \(76992586836721920\) \([2]\) \(17510400\) \(2.7696\) \(\Gamma_0(N)\)-optimal
324870.dt2 324870dt2 \([1, 1, 1, -32179771, -70553151271]\) \(-31324512477868037557921/143427974919699600\) \(-16874157821327738240400\) \([2]\) \(35020800\) \(3.1161\)  

Rank

sage: E.rank()
 

The elliptic curves in class 324870.dt have rank \(1\).

Complex multiplication

The elliptic curves in class 324870.dt do not have complex multiplication.

Modular form 324870.2.a.dt

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.