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Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1450.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1450.a1 1450b1 \([1, 1, 0, -425, 3205]\) \(-340836570625/430592\) \(-10764800\) \([]\) \(648\) \(0.25787\) \(\Gamma_0(N)\)-optimal
1450.a2 1450b2 \([1, 1, 0, 575, 15965]\) \(838699829375/4758586568\) \(-118964664200\) \([]\) \(1944\) \(0.80717\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1450.2.a.a

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