Properties

Label 440.a
Number of curves $2$
Conductor $440$
CM no
Rank $1$
Graph

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

Elliptic curves in class 440.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440.a1 440a1 \([0, 0, 0, -38, -87]\) \(379275264/15125\) \(242000\) \([2]\) \(48\) \(-0.20043\) \(\Gamma_0(N)\)-optimal
440.a2 440a2 \([0, 0, 0, 17, -318]\) \(2122416/171875\) \(-44000000\) \([2]\) \(96\) \(0.14615\)  

Rank

sage: E.rank()
 

The elliptic curves in class 440.a have rank \(1\).

Complex multiplication

The elliptic curves in class 440.a do not have complex multiplication.

Modular form 440.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 3 q^{9} - q^{11} - 8 q^{19} + O(q^{20})\) 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.