Properties

Label 16245.d
Number of curves $2$
Conductor $16245$
CM no
Rank $0$
Graph

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

Elliptic curves in class 16245.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.d1 16245l2 \([1, -1, 1, -246992, -2283816]\) \(48587168449/28048275\) \(961956183962945475\) \([2]\) \(230400\) \(2.1402\)  
16245.d2 16245l1 \([1, -1, 1, 61663, -308424]\) \(756058031/438615\) \(-15042936210120135\) \([2]\) \(115200\) \(1.7936\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16245.d have rank \(0\).

Complex multiplication

The elliptic curves in class 16245.d do not have complex multiplication.

Modular form 16245.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 3 q^{8} - q^{10} + 6 q^{11} + 2 q^{14} - q^{16} + 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.