Properties

Label 415794.y
Number of curves $2$
Conductor $415794$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 415794.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
415794.y1 415794y1 \([1, 1, 1, -37570, 2773391]\) \(39616946929/226368\) \(33510588121152\) \([2]\) \(3548160\) \(1.4367\) \(\Gamma_0(N)\)-optimal
415794.y2 415794y2 \([1, 1, 1, -16410, 5905071]\) \(-3301293169/100082952\) \(-14815868773064328\) \([2]\) \(7096320\) \(1.7833\)  

Rank

sage: E.rank()
 

The elliptic curves in class 415794.y have rank \(1\).

Complex multiplication

The elliptic curves in class 415794.y do not have complex multiplication.

Modular form 415794.2.a.y

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