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Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 62790g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.h1 62790g1 \([1, 1, 0, -5252, -112944]\) \(16026071022367561/3975095255040\) \(3975095255040\) \([2]\) \(147456\) \(1.1279\) \(\Gamma_0(N)\)-optimal
62790.h2 62790g2 \([1, 1, 0, 12668, -697136]\) \(224798965462363319/343234613030400\) \(-343234613030400\) \([2]\) \(294912\) \(1.4745\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62790.2.a.g

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