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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 72128.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.l1 | 72128bm1 | \([0, 1, 0, -1388, -19874]\) | \(39304000/1127\) | \(8485787072\) | \([2]\) | \(36864\) | \(0.68336\) | \(\Gamma_0(N)\)-optimal |
| 72128.l2 | 72128bm2 | \([0, 1, 0, 327, -64121]\) | \(8000/3703\) | \(-1784439795712\) | \([2]\) | \(73728\) | \(1.0299\) |
Rank
sage: E.rank()
The elliptic curves in class 72128.l have rank \(1\).
Complex multiplication
The elliptic curves in class 72128.l do not have complex multiplication.Modular form 72128.2.a.l
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.
