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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 43190m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43190.m2 | 43190m1 | \([1, -1, 1, -16977, -862399]\) | \(-541106281296959841/11321999360000\) | \(-11321999360000\) | \([2]\) | \(103488\) | \(1.2957\) | \(\Gamma_0(N)\)-optimal |
43190.m1 | 43190m2 | \([1, -1, 1, -272977, -54827199]\) | \(2249574551450240063841/955072563200\) | \(955072563200\) | \([2]\) | \(206976\) | \(1.6423\) |
Rank
sage: E.rank()
The elliptic curves in class 43190m have rank \(0\).
Complex multiplication
The elliptic curves in class 43190m do not have complex multiplication.Modular form 43190.2.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 Cremona 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 Cremona labels.