Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("lf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680.lf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.lf1 463680lf1 \([0, 0, 0, -3132, 18576]\) \(10536048/5635\) \(1817210142720\) \([2]\) \(737280\) \(1.0436\) \(\Gamma_0(N)\)-optimal
463680.lf2 463680lf2 \([0, 0, 0, 11988, 145584]\) \(147704148/92575\) \(-119416666521600\) \([2]\) \(1474560\) \(1.3902\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 463680.2.a.lf

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