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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 38646t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38646.bg2 | 38646t1 | \([1, -1, 1, -881, -145951]\) | \(-2797856555571/340235811392\) | \(-9186366907584\) | \([3]\) | \(84096\) | \(1.1669\) | \(\Gamma_0(N)\)-optimal |
| 38646.bg1 | 38646t2 | \([1, -1, 1, -239141, -44953271]\) | \(-76840970261960619/2083543268\) | \(-41010382144044\) | \([]\) | \(252288\) | \(1.7162\) |
Rank
sage: E.rank()
The elliptic curves in class 38646t have rank \(1\).
Complex multiplication
The elliptic curves in class 38646t do not have complex multiplication.Modular form 38646.2.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.
