Properties

Label 102.b
Number of curves $4$
Conductor $102$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102.b1 102c3 \([1, 0, 1, -751, -6046]\) \(46753267515625/11591221248\) \(11591221248\) \([2]\) \(72\) \(0.64143\)  
102.b2 102c1 \([1, 0, 1, -256, 1550]\) \(1845026709625/793152\) \(793152\) \([6]\) \(24\) \(0.092120\) \(\Gamma_0(N)\)-optimal
102.b3 102c2 \([1, 0, 1, -216, 2062]\) \(-1107111813625/1228691592\) \(-1228691592\) \([6]\) \(48\) \(0.43869\)  
102.b4 102c4 \([1, 0, 1, 1809, -37790]\) \(655215969476375/1001033261568\) \(-1001033261568\) \([2]\) \(144\) \(0.98800\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102.b have rank \(0\).

Complex multiplication

The elliptic curves in class 102.b do not have complex multiplication.

Modular form 102.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{12} + 2 q^{13} - 2 q^{14} + q^{16} - q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.