Properties

Label 132600.m
Number of curves $2$
Conductor $132600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 132600.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.m1 132600ca2 \([0, -1, 0, -780753208, 7975762062412]\) \(13158459661252114525066/745117393587651747\) \(2980469574350606988000000000\) \([2]\) \(51968000\) \(4.0264\)  
132600.m2 132600ca1 \([0, -1, 0, -769818208, 8221340292412]\) \(25226572870537521199412/88284716200629\) \(176569432401258000000000\) \([2]\) \(25984000\) \(3.6798\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 132600.m have rank \(1\).

Complex multiplication

The elliptic curves in class 132600.m do not have complex multiplication.

Modular form 132600.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - q^{13} + q^{17} - 4 q^{19} + O(q^{20})\) 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.