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Properties

Label 27200cc
Number of curves $2$
Conductor $27200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 27200cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27200.k2 27200cc1 \([0, 1, 0, -108, -962]\) \(-140608/289\) \(-289000000\) \([2]\) \(8192\) \(0.31270\) \(\Gamma_0(N)\)-optimal
27200.k1 27200cc2 \([0, 1, 0, -2233, -41337]\) \(19248832/17\) \(1088000000\) \([2]\) \(16384\) \(0.65927\)  

Rank

sage: E.rank()
 

The elliptic curves in class 27200cc have rank \(0\).

Complex multiplication

The elliptic curves in class 27200cc do not have complex multiplication.

Modular form 27200.2.a.cc

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