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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 18496t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18496.f2 | 18496t1 | \([0, 1, 0, -1252, -36810]\) | \(-140608/289\) | \(-446448476224\) | \([2]\) | \(18432\) | \(0.92459\) | \(\Gamma_0(N)\)-optimal |
| 18496.f1 | 18496t2 | \([0, 1, 0, -25817, -1604057]\) | \(19248832/17\) | \(1680747204608\) | \([2]\) | \(36864\) | \(1.2712\) |
Rank
sage: E.rank()
The elliptic curves in class 18496t have rank \(0\).
Complex multiplication
The elliptic curves in class 18496t do not have complex multiplication.Modular form 18496.2.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.
