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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 14440.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14440.n1 | 14440l2 | \([0, -1, 0, -150414380, 710089052900]\) | \(31248575021659890256/28203125\) | \(339671260820000000\) | \([2]\) | \(1612800\) | \(3.0948\) | |
| 14440.n2 | 14440l1 | \([0, -1, 0, -9398755, 11102802900]\) | \(-121981271658244096/115966796875\) | \(-87292162011718750000\) | \([2]\) | \(806400\) | \(2.7482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14440.n have rank \(0\).
Complex multiplication
The elliptic curves in class 14440.n do not have complex multiplication.Modular form 14440.2.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 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.
