Properties

Label 5445.f
Number of curves $2$
Conductor $5445$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5445.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.f1 5445l2 \([0, 0, 1, -6524562, 6414694272]\) \(-196566176333824/421875\) \(-65925403980046875\) \([3]\) \(114048\) \(2.4748\)  
5445.f2 5445l1 \([0, 0, 1, -55902, 14278635]\) \(-123633664/492075\) \(-76895391202326675\) \([]\) \(38016\) \(1.9255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5445.f have rank \(0\).

Complex multiplication

The elliptic curves in class 5445.f do not have complex multiplication.

Modular form 5445.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2q^{4} + q^{5} - q^{7} + 2q^{13} + 4q^{16} - 6q^{17} - 7q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.