Properties

Label 115520ba
Number of curves $2$
Conductor $115520$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 115520ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115520.cv1 115520ba1 \([0, -1, 0, -1330405, -550412475]\) \(5405726654464/407253125\) \(19619412024963200000\) \([2]\) \(2764800\) \(2.4472\) \(\Gamma_0(N)\)-optimal
115520.cv2 115520ba2 \([0, -1, 0, 1276015, -2446322383]\) \(298091207216/3525390625\) \(-2717370086560000000000\) \([2]\) \(5529600\) \(2.7937\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115520ba have rank \(1\).

Complex multiplication

The elliptic curves in class 115520ba do not have complex multiplication.

Modular form 115520.2.a.ba

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + 2 q^{7} + q^{9} + 6 q^{13} + 2 q^{15} + 2 q^{17} + O(q^{20})\) 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.