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Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 62790o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.m1 62790o1 \([1, 0, 1, -1450319, 672148226]\) \(337375771898029042382569/55899777024000\) \(55899777024000\) \([2]\) \(946176\) \(2.0385\) \(\Gamma_0(N)\)-optimal
62790.m2 62790o2 \([1, 0, 1, -1445839, 676508162]\) \(-334258981833828623638249/4344063071166000000\) \(-4344063071166000000\) \([2]\) \(1892352\) \(2.3850\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62790.2.a.o

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