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Properties

Label 102550.bb
Number of curves $2$
Conductor $102550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 102550.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102550.bb1 102550s1 \([1, 1, 1, -1621913, 794409031]\) \(-30198569235907907017/1932613457824\) \(-30197085278500000\) \([]\) \(2643840\) \(2.2200\) \(\Gamma_0(N)\)-optimal
102550.bb2 102550s2 \([1, 1, 1, -120288, 2192385281]\) \(-12318868629733177/132890530607693824\) \(-2076414540745216000000\) \([]\) \(7931520\) \(2.7693\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102550.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 102550.bb do not have complex multiplication.

Modular form 102550.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} - q^{7} + q^{8} + q^{9} - 6 q^{11} + 2 q^{12} + q^{13} - q^{14} + q^{16} + 3 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.