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Properties

Label 12138.t
Number of curves $3$
Conductor $12138$
CM no
Rank $0$
Graph

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

Elliptic curves in class 12138.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.t1 12138q3 \([1, 1, 1, -110311884, -446006527017]\) \(-6150311179917589675873/244053849830826\) \(-5890866640007200901994\) \([]\) \(2799360\) \(3.2607\)  
12138.t2 12138q2 \([1, 1, 1, -280914, -1548021561]\) \(-101566487155393/42823570577256\) \(-1033656889634886530664\) \([]\) \(933120\) \(2.7114\)  
12138.t3 12138q1 \([1, 1, 1, 31206, 57274023]\) \(139233463487/58763045376\) \(-1418397062413330944\) \([]\) \(311040\) \(2.1621\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12138.t have rank \(0\).

Complex multiplication

The elliptic curves in class 12138.t do not have complex multiplication.

Modular form 12138.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 5 q^{13} - q^{14} - 3 q^{15} + q^{16} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.