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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 59150.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.t1 | 59150g1 | \([1, -1, 0, -123317, -14876159]\) | \(2749884201/318500\) | \(24020916664062500\) | \([2]\) | \(387072\) | \(1.8750\) | \(\Gamma_0(N)\)-optimal |
| 59150.t2 | 59150g2 | \([1, -1, 0, 172433, -75504909]\) | \(7518017079/36968750\) | \(-2788142112792968750\) | \([2]\) | \(774144\) | \(2.2216\) |
Rank
sage: E.rank()
The elliptic curves in class 59150.t have rank \(0\).
Complex multiplication
The elliptic curves in class 59150.t do not have complex multiplication.Modular form 59150.2.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.
