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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 35739.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35739.n1 | 35739o1 | \([0, 0, 1, -88806, 11912368]\) | \(-2258403328/480491\) | \(-16479134235119259\) | \([]\) | \(259200\) | \(1.8331\) | \(\Gamma_0(N)\)-optimal |
| 35739.n2 | 35739o2 | \([0, 0, 1, 625974, -68893511]\) | \(790939860992/517504691\) | \(-17748572335991545059\) | \([]\) | \(777600\) | \(2.3824\) |
Rank
sage: E.rank()
The elliptic curves in class 35739.n have rank \(1\).
Complex multiplication
The elliptic curves in class 35739.n do not have complex multiplication.Modular form 35739.2.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.
