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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 63580.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63580.n1 | 63580j1 | \([0, -1, 0, -75525, 8505377]\) | \(-7710244864/565675\) | \(-3495428952083200\) | \([]\) | \(456192\) | \(1.7317\) | \(\Gamma_0(N)\)-optimal |
| 63580.n2 | 63580j2 | \([0, -1, 0, 433115, 6318225]\) | \(1454115454976/844421875\) | \(-5217866565868000000\) | \([]\) | \(1368576\) | \(2.2810\) |
Rank
sage: E.rank()
The elliptic curves in class 63580.n have rank \(1\).
Complex multiplication
The elliptic curves in class 63580.n do not have complex multiplication.Modular form 63580.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
