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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4650.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.t1 | 4650o2 | \([1, 0, 1, -16526, -819052]\) | \(31942518433489/27900\) | \(435937500\) | \([2]\) | \(7680\) | \(0.95814\) | |
4650.t2 | 4650o1 | \([1, 0, 1, -1026, -13052]\) | \(-7633736209/230640\) | \(-3603750000\) | \([2]\) | \(3840\) | \(0.61157\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.t have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.t do not have complex multiplication.Modular form 4650.2.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 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.