Properties

Label 283920ia
Number of curves $4$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ia1")
 
E.isogeny_class()
 

Elliptic curves in class 283920ia

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.ia4 283920ia1 \([0, 1, 0, 1465, 178608]\) \(4499456/180075\) \(-13907002090800\) \([2]\) \(589824\) \(1.2018\) \(\Gamma_0(N)\)-optimal
283920.ia3 283920ia2 \([0, 1, 0, -39940, 2927900]\) \(5702413264/275625\) \(340579643040000\) \([2, 2]\) \(1179648\) \(1.5484\)  
283920.ia1 283920ia3 \([0, 1, 0, -631440, 192917700]\) \(5633270409316/14175\) \(70062097996800\) \([2]\) \(2359296\) \(1.8949\)  
283920.ia2 283920ia4 \([0, 1, 0, -110920, -10444732]\) \(30534944836/8203125\) \(40545195600000000\) \([2]\) \(2359296\) \(1.8949\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920ia have rank \(0\).

Complex multiplication

The elliptic curves in class 283920ia do not have complex multiplication.

Modular form 283920.2.a.ia

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.