Properties

Label 485100dl
Number of curves $2$
Conductor $485100$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dl1")
 
E.isogeny_class()
 

Elliptic curves in class 485100dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
485100.dl1 485100dl1 \([0, 0, 0, -529200, 135442125]\) \(28311552/2695\) \(1560192948641250000\) \([2]\) \(9289728\) \(2.2288\) \(\Gamma_0(N)\)-optimal
485100.dl2 485100dl2 \([0, 0, 0, 628425, 645954750]\) \(2963088/21175\) \(-196138542114900000000\) \([2]\) \(18579456\) \(2.5754\)  

Rank

sage: E.rank()
 

The elliptic curves in class 485100dl have rank \(1\).

Complex multiplication

The elliptic curves in class 485100dl do not have complex multiplication.

Modular form 485100.2.a.dl

sage: E.q_eigenform(10)
 
\(q - q^{11} + 6 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.