Properties

Label 47040dd
Number of curves $4$
Conductor $47040$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 47040dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.gm4 47040dd1 \([0, 1, 0, 180, -2430]\) \(85184/405\) \(-3049462080\) \([2]\) \(24576\) \(0.50218\) \(\Gamma_0(N)\)-optimal
47040.gm3 47040dd2 \([0, 1, 0, -2025, -31977]\) \(1906624/225\) \(108425318400\) \([2, 2]\) \(49152\) \(0.84876\)  
47040.gm2 47040dd3 \([0, 1, 0, -7905, 234975]\) \(14172488/1875\) \(7228354560000\) \([2]\) \(98304\) \(1.1953\)  
47040.gm1 47040dd4 \([0, 1, 0, -31425, -2154657]\) \(890277128/15\) \(57826836480\) \([2]\) \(98304\) \(1.1953\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47040dd have rank \(0\).

Complex multiplication

The elliptic curves in class 47040dd do not have complex multiplication.

Modular form 47040.2.a.dd

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2 q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.