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Properties

Label 62790k
Number of curves $2$
Conductor $62790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 62790k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.i2 62790k1 \([1, 0, 1, -55814, -1046824]\) \(19228347883323954649/10658310664135680\) \(10658310664135680\) \([2]\) \(737280\) \(1.7659\) \(\Gamma_0(N)\)-optimal
62790.i1 62790k2 \([1, 0, 1, -677734, -214489768]\) \(34427113514311515962329/59031414877125600\) \(59031414877125600\) \([2]\) \(1474560\) \(2.1124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62790k have rank \(1\).

Complex multiplication

The elliptic curves in class 62790k do not have complex multiplication.

Modular form 62790.2.a.k

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