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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 486720t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.t2 | 486720t1 | \([0, 0, 0, 4212, -803088]\) | \(729/25\) | \(-283400935833600\) | \([2]\) | \(1769472\) | \(1.4531\) | \(\Gamma_0(N)\)-optimal* |
486720.t1 | 486720t2 | \([0, 0, 0, -108108, -13068432]\) | \(12326391/625\) | \(7085023395840000\) | \([2]\) | \(3538944\) | \(1.7997\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720t have rank \(0\).
Complex multiplication
The elliptic curves in class 486720t do not have complex multiplication.Modular form 486720.2.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.