Properties

Label 463680.eq
Number of curves $2$
Conductor $463680$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 463680.eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.eq1 463680eq1 \([0, 0, 0, -93708, -11037168]\) \(476196576129/197225\) \(37690284441600\) \([2]\) \(2359296\) \(1.5670\) \(\Gamma_0(N)\)-optimal
463680.eq2 463680eq2 \([0, 0, 0, -79308, -14545008]\) \(-288673724529/311181605\) \(-59467730791956480\) \([2]\) \(4718592\) \(1.9136\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680.eq have rank \(1\).

Complex multiplication

The elliptic curves in class 463680.eq do not have complex multiplication.

Modular form 463680.2.a.eq

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 2 q^{11} - 4 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.