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Properties

Label 424830fq
Number of curves $2$
Conductor $424830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 424830fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.fq1 424830fq1 \([1, 1, 1, -212710, 14342495]\) \(1092727/540\) \(525980505615146820\) \([2]\) \(6623232\) \(2.0934\) \(\Gamma_0(N)\)-optimal
424830.fq2 424830fq2 \([1, 1, 1, 778560, 111090447]\) \(53582633/36450\) \(-35503684129022410350\) \([2]\) \(13246464\) \(2.4400\)  

Rank

sage: E.rank()
 

The elliptic curves in class 424830fq have rank \(0\).

Complex multiplication

The elliptic curves in class 424830fq do not have complex multiplication.

Modular form 424830.2.a.fq

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} - 2 q^{13} - q^{15} + q^{16} + q^{18} + O(q^{20})\) 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.