Properties

Label 102245.d
Number of curves $2$
Conductor $102245$
CM no
Rank $1$
Graph

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

Elliptic curves in class 102245.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102245.d1 102245l1 \([1, 0, 0, -20875, -248808]\) \(117649/65\) \(555814127625185\) \([2]\) \(470400\) \(1.5198\) \(\Gamma_0(N)\)-optimal
102245.d2 102245l2 \([1, 0, 0, 81370, -1946075]\) \(6967871/4225\) \(-36127918295637025\) \([2]\) \(940800\) \(1.8664\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102245.d have rank \(1\).

Complex multiplication

The elliptic curves in class 102245.d do not have complex multiplication.

Modular form 102245.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} + q^{5} + 2 q^{6} - 4 q^{7} + 3 q^{8} + q^{9} - q^{10} + 2 q^{12} + 4 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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 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.