Properties

Label 132600t
Number of curves $4$
Conductor $132600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 132600t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.r3 132600t1 \([0, -1, 0, -11908, 431812]\) \(46689225424/7249905\) \(28999620000000\) \([2]\) \(294912\) \(1.3064\) \(\Gamma_0(N)\)-optimal
132600.r2 132600t2 \([0, -1, 0, -52408, -4185188]\) \(994958062276/98903025\) \(1582448400000000\) \([2, 2]\) \(589824\) \(1.6530\)  
132600.r4 132600t3 \([0, -1, 0, 64592, -20331188]\) \(931329171502/6107473125\) \(-195439140000000000\) \([2]\) \(1179648\) \(1.9996\)  
132600.r1 132600t4 \([0, -1, 0, -817408, -284175188]\) \(1887517194957938/21849165\) \(699173280000000\) \([2]\) \(1179648\) \(1.9996\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 132600.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4q^{11} + q^{13} - q^{17} + 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.