Properties

Label 64320i
Number of curves $2$
Conductor $64320$
CM no
Rank $0$
Graph

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

Elliptic curves in class 64320i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64320.bi2 64320i1 \([0, -1, 0, 955, 1407]\) \(1503484706816/890163675\) \(-56970475200\) \([]\) \(69120\) \(0.75317\) \(\Gamma_0(N)\)-optimal
64320.bi1 64320i2 \([0, -1, 0, -12005, -555225]\) \(-2989967081734144/380653171875\) \(-24361803000000\) \([]\) \(207360\) \(1.3025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64320i have rank \(0\).

Complex multiplication

The elliptic curves in class 64320i do not have complex multiplication.

Modular form 64320.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} + q^{9} + 6 q^{11} - 2 q^{13} - q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.