Properties

Label 62.a
Number of curves $4$
Conductor $62$
CM no
Rank $0$
Graph

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

Elliptic curves in class 62.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62.a1 62a4 \([1, -1, 1, -331, 2397]\) \(3999236143617/62\) \(62\) \([2]\) \(8\) \(-0.10808\)  
62.a2 62a3 \([1, -1, 1, -31, 5]\) \(3196010817/1847042\) \(1847042\) \([2]\) \(8\) \(-0.10808\)  
62.a3 62a2 \([1, -1, 1, -21, 41]\) \(979146657/3844\) \(3844\) \([2, 2]\) \(4\) \(-0.45465\)  
62.a4 62a1 \([1, -1, 1, -1, 1]\) \(-35937/496\) \(-496\) \([4]\) \(2\) \(-0.80122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62.a have rank \(0\).

Complex multiplication

The elliptic curves in class 62.a do not have complex multiplication.

Modular form 62.2.a.a

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.