Properties

Label 5445i
Number of curves $2$
Conductor $5445$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 5445i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.j1 5445i1 \([1, -1, 0, -14724, -414045]\) \(205379/75\) \(128920790005425\) \([2]\) \(16896\) \(1.4079\) \(\Gamma_0(N)\)-optimal
5445.j2 5445i2 \([1, -1, 0, 45171, -2965572]\) \(5929741/5625\) \(-9669059250406875\) \([2]\) \(33792\) \(1.7545\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5445i have rank \(1\).

Complex multiplication

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

Modular form 5445.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + 4 q^{13} - 2 q^{14} - q^{16} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.