Properties

Label 6720.ci
Number of curves $4$
Conductor $6720$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.ci1 6720cm3 \([0, 1, 0, -262305, 51618303]\) \(60910917333827912/3255076125\) \(106662334464000\) \([4]\) \(36864\) \(1.7591\)  
6720.ci2 6720cm2 \([0, 1, 0, -17305, 707303]\) \(139927692143296/27348890625\) \(112021056000000\) \([2, 2]\) \(18432\) \(1.4126\)  
6720.ci3 6720cm1 \([0, 1, 0, -5300, -140250]\) \(257307998572864/19456203375\) \(1245197016000\) \([2]\) \(9216\) \(1.0660\) \(\Gamma_0(N)\)-optimal
6720.ci4 6720cm4 \([0, 1, 0, 35615, 4231775]\) \(152461584507448/322998046875\) \(-10584000000000000\) \([2]\) \(36864\) \(1.7591\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6720.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 6720.ci do not have complex multiplication.

Modular form 6720.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} - 4q^{11} - 2q^{13} + q^{15} - 2q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.