Properties

Label 65520.i
Number of curves $2$
Conductor $65520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 65520.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65520.i1 65520bt2 \([0, 0, 0, -852843, 303144858]\) \(620307836233921107/2548000000\) \(281788416000000\) \([2]\) \(589824\) \(1.9826\)  
65520.i2 65520bt1 \([0, 0, 0, -54123, 4583322]\) \(158542456758867/9691136000\) \(1071762112512000\) \([2]\) \(294912\) \(1.6360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 65520.i have rank \(0\).

Complex multiplication

The elliptic curves in class 65520.i do not have complex multiplication.

Modular form 65520.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 2 q^{11} - q^{13} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.