Properties

Label 1638.t
Number of curves $2$
Conductor $1638$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1638.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.t1 1638n2 \([1, -1, 1, -191, -1511]\) \(-38958219/30758\) \(-605409714\) \([]\) \(864\) \(0.38364\)  
1638.t2 1638n1 \([1, -1, 1, 19, 29]\) \(29503629/35672\) \(-963144\) \([3]\) \(288\) \(-0.16566\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1638.t have rank \(0\).

Complex multiplication

The elliptic curves in class 1638.t do not have complex multiplication.

Modular form 1638.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 3q^{11} + q^{13} + q^{14} + q^{16} - 3q^{17} + 5q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.