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Properties

Label 254898dj
Number of curves $2$
Conductor $254898$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 254898dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254898.dj1 254898dj1 \([1, -1, 0, -1319628, 583868872]\) \(-67645179/8\) \(-30056028892294104\) \([]\) \(4644864\) \(2.1873\) \(\Gamma_0(N)\)-optimal
254898.dj2 254898dj2 \([1, -1, 0, 167277, 1801445813]\) \(189/512\) \(-1402294083998873716224\) \([]\) \(13934592\) \(2.7366\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254898dj have rank \(1\).

Complex multiplication

The elliptic curves in class 254898dj do not have complex multiplication.

Modular form 254898.2.a.dj

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} - 3 q^{11} + 2 q^{13} + q^{16} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.