Properties

Label 54720cc
Number of curves $4$
Conductor $54720$
CM no
Rank $0$
Graph

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

Elliptic curves in class 54720cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.ea4 54720cc1 \([0, 0, 0, 708, -12656]\) \(3286064/7695\) \(-91908587520\) \([2]\) \(49152\) \(0.78768\) \(\Gamma_0(N)\)-optimal
54720.ea3 54720cc2 \([0, 0, 0, -5772, -139664]\) \(445138564/81225\) \(3880584806400\) \([2, 2]\) \(98304\) \(1.1342\)  
54720.ea2 54720cc3 \([0, 0, 0, -27372, 1614256]\) \(23735908082/1954815\) \(186785482014720\) \([4]\) \(196608\) \(1.4808\)  
54720.ea1 54720cc4 \([0, 0, 0, -87852, -10022096]\) \(784767874322/35625\) \(3404021760000\) \([2]\) \(196608\) \(1.4808\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54720cc have rank \(0\).

Complex multiplication

The elliptic curves in class 54720cc do not have complex multiplication.

Modular form 54720.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{11} - 2 q^{13} - 6 q^{17} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.