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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 283920.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.n1 | 283920n2 | \([0, -1, 0, -3158346416, 68318196095616]\) | \(80214500261567905813/1722980109375\) | \(74839414741232266944000000\) | \([2]\) | \(172523520\) | \(4.0816\) | |
| 283920.n2 | 283920n1 | \([0, -1, 0, -204348096, 988303187520]\) | \(21726280496903653/2860061896125\) | \(124229732696878094866944000\) | \([2]\) | \(86261760\) | \(3.7351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 283920.n have rank \(1\).
Complex multiplication
The elliptic curves in class 283920.n do not have complex multiplication.Modular form 283920.2.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.
