Properties

Label 110400cm
Number of curves $2$
Conductor $110400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 110400cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110400.bg1 110400cm1 \([0, -1, 0, -3708, -85338]\) \(45118016/207\) \(25875000000\) \([2]\) \(81920\) \(0.84883\) \(\Gamma_0(N)\)-optimal
110400.bg2 110400cm2 \([0, -1, 0, -1833, -173463]\) \(-85184/1587\) \(-12696000000000\) \([2]\) \(163840\) \(1.1954\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110400cm have rank \(1\).

Complex multiplication

The elliptic curves in class 110400cm do not have complex multiplication.

Modular form 110400.2.a.cm

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