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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 54978.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.m1 | 54978l2 | \([1, 1, 0, -60099, 3249765]\) | \(204055591784617/78708537864\) | \(9259980771161736\) | \([2]\) | \(483840\) | \(1.7627\) | |
54978.m2 | 54978l1 | \([1, 1, 0, -26779, -1661603]\) | \(18052771191337/444958272\) | \(52348895742528\) | \([2]\) | \(241920\) | \(1.4161\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54978.m have rank \(0\).
Complex multiplication
The elliptic curves in class 54978.m do not have complex multiplication.Modular form 54978.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.