Properties

Label 494190.cm
Number of curves $2$
Conductor $494190$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 494190.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
494190.cm1 494190cm2 \([1, -1, 0, -78084, 8285490]\) \(2992209121/54150\) \(952838984424150\) \([2]\) \(3194880\) \(1.6695\) \(\Gamma_0(N)\)-optimal*
494190.cm2 494190cm1 \([1, -1, 0, -54, 373248]\) \(-1/3420\) \(-60179304279420\) \([2]\) \(1597440\) \(1.3229\) \(\Gamma_0(N)\)-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 494190.cm1.

Rank

sage: E.rank()
 

The elliptic curves in class 494190.cm have rank \(0\).

Complex multiplication

The elliptic curves in class 494190.cm do not have complex multiplication.

Modular form 494190.2.a.cm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} + 6 q^{13} - 2 q^{14} + q^{16} + q^{19} + O(q^{20})\) 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.