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Properties

Label 101430cc
Number of curves $2$
Conductor $101430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 101430cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.ci2 101430cc1 \([1, -1, 0, -4021929, 2976305485]\) \(83890194895342081/3958384640000\) \(339495295998781440000\) \([2]\) \(5160960\) \(2.7002\) \(\Gamma_0(N)\)-optimal
101430.ci1 101430cc2 \([1, -1, 0, -11077929, -10315787315]\) \(1753007192038126081/478174101507200\) \(41011137848932797571200\) \([2]\) \(10321920\) \(3.0468\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430cc have rank \(0\).

Complex multiplication

The elliptic curves in class 101430cc do not have complex multiplication.

Modular form 101430.2.a.cc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 2 q^{11} + 4 q^{13} + q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.