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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 443760t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 443760.t1 | 443760t1 | \([0, -1, 0, -666256, 205344256]\) | \(1263214441/29025\) | \(751524095988633600\) | \([2]\) | \(8515584\) | \(2.2164\) | \(\Gamma_0(N)\)-optimal |
| 443760.t2 | 443760t2 | \([0, -1, 0, 73344, 635495616]\) | \(1685159/6739605\) | \(-174503895088560721920\) | \([2]\) | \(17031168\) | \(2.5630\) |
Rank
sage: E.rank()
The elliptic curves in class 443760t have rank \(1\).
Complex multiplication
The elliptic curves in class 443760t do not have complex multiplication.Modular form 443760.2.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.
