Properties

Label 27720i
Number of curves $2$
Conductor $27720$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 27720i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27720.v1 27720i1 \([0, 0, 0, -1083, -13498]\) \(188183524/3465\) \(2586608640\) \([2]\) \(18432\) \(0.60076\) \(\Gamma_0(N)\)-optimal
27720.v2 27720i2 \([0, 0, 0, -3, -39202]\) \(-2/444675\) \(-663896217600\) \([2]\) \(36864\) \(0.94733\)  

Rank

sage: E.rank()
 

The elliptic curves in class 27720i have rank \(0\).

Complex multiplication

The elliptic curves in class 27720i do not have complex multiplication.

Modular form 27720.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + q^{11} - 8 q^{17} + 8 q^{19} + O(q^{20})\) 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.