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Properties

Label 294350.cm
Number of curves $2$
Conductor $294350$
CM no
Rank $0$
Graph

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

Elliptic curves in class 294350.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
294350.cm1 294350cm2 \([1, 0, 0, -38283, -4054333]\) \(-417267265/235298\) \(-3499018444616450\) \([]\) \(1741824\) \(1.6858\)  
294350.cm2 294350cm1 \([1, 0, 0, 3767, 74977]\) \(397535/392\) \(-5829268545800\) \([]\) \(580608\) \(1.1365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 294350.cm have rank \(0\).

Complex multiplication

The elliptic curves in class 294350.cm do not have complex multiplication.

Modular form 294350.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} - 2 q^{9} - 3 q^{11} + q^{12} - 2 q^{13} - q^{14} + q^{16} + 3 q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.