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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 147294bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 147294.f2 | 147294bt1 | \([1, -1, 0, -119961, 16020661]\) | \(2226025896193/252504\) | \(21656288616984\) | \([]\) | \(1069056\) | \(1.5865\) | \(\Gamma_0(N)\)-optimal |
| 147294.f1 | 147294bt2 | \([1, -1, 0, -265491, -29419097]\) | \(24130052890273/9585058854\) | \(822073317464285334\) | \([]\) | \(3207168\) | \(2.1358\) |
Rank
sage: E.rank()
The elliptic curves in class 147294bt have rank \(1\).
Complex multiplication
The elliptic curves in class 147294bt do not have complex multiplication.Modular form 147294.2.a.bt
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.
