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Properties

Label 65366.t
Number of curves $2$
Conductor $65366$
CM no
Rank $0$
Graph

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

Elliptic curves in class 65366.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65366.t1 65366r2 \([1, 1, 1, -18033, 13523]\) \(5512402554625/3188422748\) \(375114747879452\) \([2]\) \(258048\) \(1.4860\)  
65366.t2 65366r1 \([1, 1, 1, 4507, 4507]\) \(86058173375/49827568\) \(-5862163547632\) \([2]\) \(129024\) \(1.1394\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 65366.t have rank \(0\).

Complex multiplication

The elliptic curves in class 65366.t do not have complex multiplication.

Modular form 65366.2.a.t

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