Properties

Label 49419f
Number of curves $3$
Conductor $49419$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 49419f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49419.j3 49419f1 \([0, 0, 1, 1734, 1228]\) \(32768/19\) \(-334329468219\) \([]\) \(40320\) \(0.90074\) \(\Gamma_0(N)\)-optimal
49419.j2 49419f2 \([0, 0, 1, -24276, 1548823]\) \(-89915392/6859\) \(-120692938027059\) \([]\) \(120960\) \(1.4500\)  
49419.j1 49419f3 \([0, 0, 1, -2001036, 1089508108]\) \(-50357871050752/19\) \(-334329468219\) \([]\) \(362880\) \(1.9994\)  

Rank

sage: E.rank()
 

The elliptic curves in class 49419f have rank \(1\).

Complex multiplication

The elliptic curves in class 49419f do not have complex multiplication.

Modular form 49419.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2q^{4} + 3q^{5} + q^{7} + 3q^{11} - 4q^{13} + 4q^{16} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.