Properties

Label 44100.n
Number of curves $2$
Conductor $44100$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.n1 44100q1 \([0, 0, 0, -37800, -2811375]\) \(3538944/25\) \(42195431250000\) \([2]\) \(110592\) \(1.4471\) \(\Gamma_0(N)\)-optimal
44100.n2 44100q2 \([0, 0, 0, -14175, -6284250]\) \(-11664/625\) \(-16878172500000000\) \([2]\) \(221184\) \(1.7936\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44100.n have rank \(1\).

Complex multiplication

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

Modular form 44100.2.a.n

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