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Properties

Label 462550.t
Number of curves $2$
Conductor $462550$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462550.t have rank \(1\).

Complex multiplication

The elliptic curves in class 462550.t do not have complex multiplication.

Modular form 462550.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 5 q^{7} - q^{8} - 2 q^{9} - q^{11} + q^{12} - 2 q^{13} + 5 q^{14} + q^{16} + 3 q^{17} + 2 q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 462550.t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462550.t1 462550t1 \([1, 0, 1, -1861151, 986459698]\) \(-76711450249/851840\) \(-7917098402510000000\) \([]\) \(16765056\) \(2.4412\) \(\Gamma_0(N)\)-optimal
462550.t2 462550t2 \([1, 0, 1, 6233474, 5114718448]\) \(2882081488391/2883584000\) \(-26800359550976000000000\) \([]\) \(50295168\) \(2.9905\)