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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 24882t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.v1 | 24882t1 | \([1, 0, 1, -182, 32942]\) | \(-661459323097/468850704894\) | \(-468850704894\) | \([3]\) | \(36288\) | \(0.91852\) | \(\Gamma_0(N)\)-optimal |
24882.v2 | 24882t2 | \([1, 0, 1, 1633, -889078]\) | \(482019393285143/341861913811704\) | \(-341861913811704\) | \([]\) | \(108864\) | \(1.4678\) |
Rank
sage: E.rank()
The elliptic curves in class 24882t have rank \(0\).
Complex multiplication
The elliptic curves in class 24882t do not have complex multiplication.Modular form 24882.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.