Properties

Label 33150.t
Number of curves $2$
Conductor $33150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 33150.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.t1 33150bb2 \([1, 0, 1, -232076, -43030702]\) \(3538764637823065/1969338072\) \(769272684375000\) \([]\) \(233280\) \(1.8039\)  
33150.t2 33150bb1 \([1, 0, 1, -8951, 255548]\) \(203005872265/44836038\) \(17514077343750\) \([3]\) \(77760\) \(1.2546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33150.t have rank \(1\).

Complex multiplication

The elliptic curves in class 33150.t do not have complex multiplication.

Modular form 33150.2.a.t

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