Properties

Label 442225v
Number of curves $2$
Conductor $442225$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 442225v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
442225.v2 442225v1 \([1, 1, 1, -72388, -8192094]\) \(-9317\) \(-4502437830078125\) \([]\) \(1572480\) \(1.7420\) \(\Gamma_0(N)\)-optimal*
442225.v1 442225v2 \([1, 1, 1, -1877949263, 31322978082906]\) \(-162677523113838677\) \(-4502437830078125\) \([]\) \(58181760\) \(3.5474\) \(\Gamma_0(N)\)-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 442225v1.

Rank

sage: E.rank()
 

The elliptic curves in class 442225v have rank \(0\).

Complex multiplication

The elliptic curves in class 442225v do not have complex multiplication.

Modular form 442225.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{8} - 2 q^{9} + q^{12} + 2 q^{13} - q^{16} - 2 q^{17} + 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.