Properties

Label 258570.dc
Number of curves $2$
Conductor $258570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 258570.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
258570.dc1 258570dc1 \([1, -1, 1, -26903, -755153]\) \(611960049/282880\) \(995382235111680\) \([2]\) \(1376256\) \(1.5725\) \(\Gamma_0(N)\)-optimal
258570.dc2 258570dc2 \([1, -1, 1, 94777, -5768369]\) \(26757728271/19536400\) \(-68743585612400400\) \([2]\) \(2752512\) \(1.9191\)  

Rank

sage: E.rank()
 

The elliptic curves in class 258570.dc have rank \(1\).

Complex multiplication

The elliptic curves in class 258570.dc do not have complex multiplication.

Modular form 258570.2.a.dc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + q^{16} - q^{17} + 6 q^{19} + O(q^{20})\) 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.