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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 154560ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.gz1 | 154560ep1 | \([0, 1, 0, -4222065, 3214889775]\) | \(508017439289666674384/21234429931640625\) | \(347904900000000000000\) | \([2]\) | \(6881280\) | \(2.7064\) | \(\Gamma_0(N)\)-optimal |
| 154560.gz2 | 154560ep2 | \([0, 1, 0, 2027935, 11926139775]\) | \(14073614784514581404/945607964406328125\) | \(-61971363555333120000000\) | \([2]\) | \(13762560\) | \(3.0530\) |
Rank
sage: E.rank()
The elliptic curves in class 154560ep have rank \(0\).
Complex multiplication
The elliptic curves in class 154560ep do not have complex multiplication.Modular form 154560.2.a.ep
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
