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Properties

Label 93138m
Number of curves $2$
Conductor $93138$
CM no
Rank $0$
Graph

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

Elliptic curves in class 93138m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93138.k2 93138m1 \([1, 0, 1, -31548, -2159318]\) \(506242516969099/11449008\) \(78528745872\) \([2]\) \(514560\) \(1.2046\) \(\Gamma_0(N)\)-optimal
93138.k1 93138m2 \([1, 0, 1, -32688, -1995158]\) \(563130251390539/75856356588\) \(520298749837092\) \([2]\) \(1029120\) \(1.5512\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93138m have rank \(0\).

Complex multiplication

The elliptic curves in class 93138m do not have complex multiplication.

Modular form 93138.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + 4 q^{10} + 4 q^{11} + q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{15} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) 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.