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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 227154.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227154.m1 | 227154i2 | \([1, 1, 1, -65616011, -204606903193]\) | \(1294373635812597347281/2083292441154\) | \(50285615045533114626\) | \([]\) | \(18480000\) | \(3.0447\) | |
227154.m2 | 227154i1 | \([1, 1, 1, -617021, 177057587]\) | \(1076291879750641/60150618144\) | \(1451889695843451936\) | \([]\) | \(3696000\) | \(2.2400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227154.m have rank \(0\).
Complex multiplication
The elliptic curves in class 227154.m do not have complex multiplication.Modular form 227154.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.