Properties

Label 236992.m
Number of curves $2$
Conductor $236992$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.m1 236992m2 \([0, 1, 0, -20500513, -33454460865]\) \(24553362849625/1755162752\) \(68112109622265519276032\) \([2]\) \(22708224\) \(3.1282\)  
236992.m2 236992m1 \([0, 1, 0, 1167327, -2283106241]\) \(4533086375/60669952\) \(-2354401844896026591232\) \([2]\) \(11354112\) \(2.7816\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.m have rank \(2\).

Complex multiplication

The elliptic curves in class 236992.m do not have complex multiplication.

Modular form 236992.2.a.m

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