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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 294350j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
294350.j2 | 294350j1 | \([1, 1, 0, 94175, 9372125]\) | \(397535/392\) | \(-91082321028125000\) | \([]\) | \(2903040\) | \(1.9412\) | \(\Gamma_0(N)\)-optimal |
294350.j1 | 294350j2 | \([1, 1, 0, -957075, -506791625]\) | \(-417267265/235298\) | \(-54672163197132031250\) | \([]\) | \(8709120\) | \(2.4905\) |
Rank
sage: E.rank()
The elliptic curves in class 294350j have rank \(1\).
Complex multiplication
The elliptic curves in class 294350j do not have complex multiplication.Modular form 294350.2.a.j
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.