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Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 62790e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.d1 62790e1 \([1, 1, 0, -26708, 1543248]\) \(2107042143459526729/175603838592000\) \(175603838592000\) \([2]\) \(276480\) \(1.4753\) \(\Gamma_0(N)\)-optimal
62790.d2 62790e2 \([1, 1, 0, 28172, 7130032]\) \(2472593161916542391/23320384951500000\) \(-23320384951500000\) \([2]\) \(552960\) \(1.8219\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62790.2.a.e

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