Properties

Label 2448t
Number of curves $2$
Conductor $2448$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2448t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2448.t1 2448t1 \([0, 0, 0, -363, 1690]\) \(1771561/612\) \(1827422208\) \([2]\) \(1536\) \(0.47893\) \(\Gamma_0(N)\)-optimal
2448.t2 2448t2 \([0, 0, 0, 1077, 11770]\) \(46268279/46818\) \(-139797798912\) \([2]\) \(3072\) \(0.82550\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2448t have rank \(0\).

Complex multiplication

The elliptic curves in class 2448t do not have complex multiplication.

Modular form 2448.2.a.t

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + 2 q^{7} - 6 q^{13} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.