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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 200277.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200277.m1 | 200277n1 | \([1, -1, 1, -2786159, -525161042]\) | \(5034501056619/2662043923\) | \(1264736457216299249721\) | \([2]\) | \(7962624\) | \(2.7406\) | \(\Gamma_0(N)\)-optimal |
200277.m2 | 200277n2 | \([1, -1, 1, 10595986, -4111575902]\) | \(276925569324741/175609527247\) | \(-83432046114965606773869\) | \([2]\) | \(15925248\) | \(3.0872\) |
Rank
sage: E.rank()
The elliptic curves in class 200277.m have rank \(1\).
Complex multiplication
The elliptic curves in class 200277.m do not have complex multiplication.Modular form 200277.2.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.