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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 32368.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32368.t1 | 32368v1 | \([0, 0, 0, -3512795, -2393878902]\) | \(9869198625/614656\) | \(298560511246909571072\) | \([2]\) | \(835584\) | \(2.6802\) | \(\Gamma_0(N)\)-optimal |
| 32368.t2 | 32368v2 | \([0, 0, 0, 2775845, -10027030134]\) | \(4869777375/92236816\) | \(-44802736718989367508992\) | \([2]\) | \(1671168\) | \(3.0268\) |
Rank
sage: E.rank()
The elliptic curves in class 32368.t have rank \(1\).
Complex multiplication
The elliptic curves in class 32368.t do not have complex multiplication.Modular form 32368.2.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 LMFDB 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 LMFDB labels.
