Properties

Label 44100bz
Number of curves $2$
Conductor $44100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 44100bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.t2 44100bz1 \([0, 0, 0, -14700, -2786875]\) \(-16384/147\) \(-3151904946750000\) \([2]\) \(184320\) \(1.6564\) \(\Gamma_0(N)\)-optimal
44100.t1 44100bz2 \([0, 0, 0, -400575, -97326250]\) \(20720464/63\) \(21613062492000000\) \([2]\) \(368640\) \(2.0030\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44100bz have rank \(0\).

Complex multiplication

The elliptic curves in class 44100bz do not have complex multiplication.

Modular form 44100.2.a.bz

sage: E.q_eigenform(10)
 
\(q - 2 q^{11} - 6 q^{13} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.