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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 320892n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320892.n1 | 320892n1 | \([0, 1, 0, -151169, -22672608]\) | \(13478411517952/304317\) | \(8625858061392\) | \([2]\) | \(1344000\) | \(1.5963\) | \(\Gamma_0(N)\)-optimal |
| 320892.n2 | 320892n2 | \([0, 1, 0, -145724, -24375804]\) | \(-754612278352/127035441\) | \(-57613064420710656\) | \([2]\) | \(2688000\) | \(1.9428\) |
Rank
sage: E.rank()
The elliptic curves in class 320892n have rank \(0\).
Complex multiplication
The elliptic curves in class 320892n do not have complex multiplication.Modular form 320892.2.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.
