Properties

Label 485100co
Number of curves $2$
Conductor $485100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 485100co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
485100.co2 485100co1 \([0, 0, 0, 2366700, 594547625]\) \(199344128/136125\) \(-1001123808711468750000\) \([2]\) \(15482880\) \(2.7183\) \(\Gamma_0(N)\)-optimal*
485100.co1 485100co2 \([0, 0, 0, -10367175, 4962266750]\) \(1047213232/515625\) \(60674170224937500000000\) \([2]\) \(30965760\) \(3.0648\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 485100co1.

Rank

sage: E.rank()
 

The elliptic curves in class 485100co have rank \(0\).

Complex multiplication

The elliptic curves in class 485100co do not have complex multiplication.

Modular form 485100.2.a.co

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