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Properties

Label 230115.d
Number of curves $2$
Conductor $230115$
CM no
Rank $0$
Graph

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

Elliptic curves in class 230115.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230115.d1 230115d2 \([1, 1, 1, -730031, -240324856]\) \(290656902035521/86293125\) \(12774479473963125\) \([2]\) \(3108864\) \(2.0690\)  
230115.d2 230115d1 \([1, 1, 1, -39686, -4779142]\) \(-46694890801/39169575\) \(-5798502856877175\) \([2]\) \(1554432\) \(1.7225\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 230115.d have rank \(0\).

Complex multiplication

The elliptic curves in class 230115.d do not have complex multiplication.

Modular form 230115.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + q^{15} - q^{16} - 4 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.