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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 11600t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11600.g2 | 11600t1 | \([0, -1, 0, 1992, -57488]\) | \(13651919/29696\) | \(-1900544000000\) | \([]\) | \(13440\) | \(1.0403\) | \(\Gamma_0(N)\)-optimal |
11600.g1 | 11600t2 | \([0, -1, 0, -182008, 30150512]\) | \(-10418796526321/82044596\) | \(-5250854144000000\) | \([]\) | \(67200\) | \(1.8450\) |
Rank
sage: E.rank()
The elliptic curves in class 11600t have rank \(0\).
Complex multiplication
The elliptic curves in class 11600t do not have complex multiplication.Modular form 11600.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.