Properties

Label 463680er
Number of curves $2$
Conductor $463680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("er1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.er1 463680er1 \([0, 0, 0, -13548, -334672]\) \(1439069689/579600\) \(110763284889600\) \([2]\) \(1179648\) \(1.3928\) \(\Gamma_0(N)\)-optimal
463680.er2 463680er2 \([0, 0, 0, 44052, -2431312]\) \(49471280711/41992020\) \(-8024799990251520\) \([2]\) \(2359296\) \(1.7394\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680er have rank \(0\).

Complex multiplication

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

Modular form 463680.2.a.er

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