Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.u1 44100by2 \([0, 0, 0, -9975, -355250]\) \(109744/9\) \(9001692000000\) \([2]\) \(98304\) \(1.2282\)  
44100.u2 44100by1 \([0, 0, 0, -2100, 30625]\) \(16384/3\) \(187535250000\) \([2]\) \(49152\) \(0.88167\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44100.u have rank \(2\).

Complex multiplication

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

Modular form 44100.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{11} - 4 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.