Properties

Label 47652.d
Number of curves $2$
Conductor $47652$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 47652.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47652.d1 47652c1 \([0, -1, 0, -48133, -4067855]\) \(-1024000000/5643\) \(-67962856059648\) \([]\) \(129600\) \(1.4975\) \(\Gamma_0(N)\)-optimal
47652.d2 47652c2 \([0, -1, 0, 125147, -21794399]\) \(17997824000/27387987\) \(-329853946171276032\) \([]\) \(388800\) \(2.0468\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47652.d have rank \(1\).

Complex multiplication

The elliptic curves in class 47652.d do not have complex multiplication.

Modular form 47652.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} - q^{11} - 5 q^{13} + 3 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.