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Properties

Label 24546d
Number of curves $2$
Conductor $24546$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 24546d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24546.f1 24546d1 \([1, 1, 1, -20028, 1078173]\) \(888459868425138625/4169612132352\) \(4169612132352\) \([2]\) \(60720\) \(1.2714\) \(\Gamma_0(N)\)-optimal
24546.f2 24546d2 \([1, 1, 1, -9788, 2192285]\) \(-103707070675890625/2023957825062912\) \(-2023957825062912\) \([2]\) \(121440\) \(1.6180\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24546d have rank \(0\).

Complex multiplication

The elliptic curves in class 24546d do not have complex multiplication.

Modular form 24546.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{12} - 2 q^{13} + 4 q^{14} + q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.