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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)
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.