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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1122n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1122.n1 | 1122n1 | \([1, 0, 0, -196, -1072]\) | \(832972004929/610368\) | \(610368\) | \([2]\) | \(384\) | \(0.044368\) | \(\Gamma_0(N)\)-optimal |
1122.n2 | 1122n2 | \([1, 0, 0, -156, -1512]\) | \(-420021471169/727634952\) | \(-727634952\) | \([2]\) | \(768\) | \(0.39094\) |
Rank
sage: E.rank()
The elliptic curves in class 1122n have rank \(0\).
Complex multiplication
The elliptic curves in class 1122n do not have complex multiplication.Modular form 1122.2.a.n
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.