Properties

Label 1450.d
Number of curves $2$
Conductor $1450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1450.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1450.d1 1450c2 \([1, 1, 0, -5950, -182250]\) \(-2386099825/48778\) \(-476347656250\) \([]\) \(3240\) \(1.0325\)  
1450.d2 1450c1 \([1, 1, 0, 300, -1000]\) \(304175/232\) \(-2265625000\) \([]\) \(1080\) \(0.48320\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1450.d have rank \(1\).

Complex multiplication

The elliptic curves in class 1450.d do not have complex multiplication.

Modular form 1450.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.