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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 20286t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20286.r2 | 20286t1 | \([1, -1, 0, -3852, -92016]\) | \(-25282750375/304704\) | \(-76190321088\) | \([2]\) | \(18432\) | \(0.89972\) | \(\Gamma_0(N)\)-optimal |
20286.r1 | 20286t2 | \([1, -1, 0, -61812, -5899608]\) | \(104453838382375/14904\) | \(3726700488\) | \([2]\) | \(36864\) | \(1.2463\) |
Rank
sage: E.rank()
The elliptic curves in class 20286t have rank \(1\).
Complex multiplication
The elliptic curves in class 20286t do not have complex multiplication.Modular form 20286.2.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.