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Properties

Label 19890m
Number of curves $2$
Conductor $19890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 19890m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19890.c1 19890m1 \([1, -1, 0, -195255, -33264675]\) \(-1129285954562528881/4130500608000\) \(-3011134943232000\) \([]\) \(207360\) \(1.8309\) \(\Gamma_0(N)\)-optimal
19890.c2 19890m2 \([1, -1, 0, 431145, -174256515]\) \(12158099101398341519/25007954601383520\) \(-18230798904408586080\) \([3]\) \(622080\) \(2.3802\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19890m have rank \(0\).

Complex multiplication

The elliptic curves in class 19890m do not have complex multiplication.

Modular form 19890.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.