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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 193600.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.t1 | 193600s2 | \([0, 1, 0, -125033, 11395063]\) | \(1906624/605\) | \(68594841920000000\) | \([2]\) | \(2211840\) | \(1.9345\) | |
193600.t2 | 193600s1 | \([0, 1, 0, -49408, -4108062]\) | \(7529536/275\) | \(487179275000000\) | \([2]\) | \(1105920\) | \(1.5879\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193600.t have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.t do not have complex multiplication.Modular form 193600.2.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.