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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 40560f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.i1 | 40560f1 | \([0, -1, 0, -27096, -1338624]\) | \(202612/45\) | \(488655331107840\) | \([2]\) | \(179712\) | \(1.5318\) | \(\Gamma_0(N)\)-optimal |
| 40560.i2 | 40560f2 | \([0, -1, 0, 60784, -8298720]\) | \(1143574/2025\) | \(-43978979799705600\) | \([2]\) | \(359424\) | \(1.8784\) |
Rank
sage: E.rank()
The elliptic curves in class 40560f have rank \(0\).
Complex multiplication
The elliptic curves in class 40560f do not have complex multiplication.Modular form 40560.2.a.f
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.
