Properties

Label 6160.a
Number of curves $2$
Conductor $6160$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6160.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.a1 6160h2 \([0, 1, 0, -1176, 15124]\) \(43949604889/42350\) \(173465600\) \([2]\) \(3072\) \(0.50213\)  
6160.a2 6160h1 \([0, 1, 0, -56, 340]\) \(-4826809/10780\) \(-44154880\) \([2]\) \(1536\) \(0.15556\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6160.a have rank \(1\).

Complex multiplication

The elliptic curves in class 6160.a do not have complex multiplication.

Modular form 6160.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 2q^{13} + 2q^{15} + 2q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.