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Properties

Label 129360.ib
Number of curves $2$
Conductor $129360$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ib1")
 
E.isogeny_class()
 

Elliptic curves in class 129360.ib

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.ib1 129360id2 \([0, 1, 0, -659605, -206422525]\) \(-65860951343104/3493875\) \(-1683664485888000\) \([]\) \(1492992\) \(1.9895\)  
129360.ib2 129360id1 \([0, 1, 0, -1045, -754237]\) \(-262144/509355\) \(-245453235793920\) \([]\) \(497664\) \(1.4401\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 129360.ib have rank \(0\).

Complex multiplication

The elliptic curves in class 129360.ib do not have complex multiplication.

Modular form 129360.2.a.ib

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + q^{11} + 4 q^{13} + q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) 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 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.