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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 27584.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.m1 | 27584f2 | \([0, -1, 0, -4609, -888319]\) | \(-41314084993/1281007856\) | \(-335808523403264\) | \([]\) | \(82944\) | \(1.4677\) | |
27584.m2 | 27584f1 | \([0, -1, 0, 511, 32257]\) | \(56181887/1765376\) | \(-462782726144\) | \([]\) | \(27648\) | \(0.91838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27584.m have rank \(1\).
Complex multiplication
The elliptic curves in class 27584.m do not have complex multiplication.Modular form 27584.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.