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Properties

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

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Show commands: SageMath
E = EllipticCurve("ic1")
 
E.isogeny_class()
 

Elliptic curves in class 254898.ic

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254898.ic1 254898ic2 \([1, -1, 1, -1850666, 974446953]\) \(-16591834777/98304\) \(-4153214927850799104\) \([]\) \(7464960\) \(2.4128\)  
254898.ic2 254898ic1 \([1, -1, 1, 61069, 7109043]\) \(596183/864\) \(-36502865576813664\) \([]\) \(2488320\) \(1.8635\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 254898.2.a.ic

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