↑

Properties

Label 444675bj
Number of curves $2$
Conductor $444675$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 444675bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444675.bj2 444675bj1 \([0, 1, 1, -1325180908, 21744015290344]\) \(-79028701534867456/16987307596875\) \(-55320860635072475603466796875\) \([]\) \(829440000\) \(4.2364\) \(\Gamma_0(N)\)-optimal
444675.bj1 444675bj2 \([0, 1, 1, -3970997158, -1820911366584656]\) \(-2126464142970105856/438611057788643355\) \(-1428380634338483893179283728046875\) \([]\) \(4147200000\) \(5.0411\)  

Rank

sage: E.rank()
 

The elliptic curves in class 444675bj have rank \(0\).

Complex multiplication

The elliptic curves in class 444675bj do not have complex multiplication.

Modular form 444675.2.a.bj

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{9} + 2 q^{12} + 6 q^{13} - 4 q^{16} + 7 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.