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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 109200m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
109200.cj1 | 109200m1 | \([0, -1, 0, -491408, 62583312]\) | \(820221748268836/369468094905\) | \(5911489518480000000\) | \([2]\) | \(1806336\) | \(2.2972\) | \(\Gamma_0(N)\)-optimal |
109200.cj2 | 109200m2 | \([0, -1, 0, 1705592, 466831312]\) | \(17147425715207422/12872524043925\) | \(-411920769405600000000\) | \([2]\) | \(3612672\) | \(2.6438\) |
Rank
sage: E.rank()
The elliptic curves in class 109200m have rank \(0\).
Complex multiplication
The elliptic curves in class 109200m do not have complex multiplication.Modular form 109200.2.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.