Properties

Label 248430v
Number of curves $2$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 248430v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.v1 248430v1 \([1, 1, 0, -1138634123, -14788983971523]\) \(98610250747761380828647/47309184000\) \(78324871524052608000\) \([2]\) \(72253440\) \(3.5896\) \(\Gamma_0(N)\)-optimal
248430.v2 248430v2 \([1, 1, 0, -1138444843, -14794146356387]\) \(-98561081716303113792487/68303188804500000\) \(-113082451132439125291500000\) \([2]\) \(144506880\) \(3.9361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 248430v have rank \(0\).

Complex multiplication

The elliptic curves in class 248430v do not have complex multiplication.

Modular form 248430.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} + q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.