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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 164730cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164730.r2 | 164730cn1 | \([1, 1, 0, 1877483, 316761271]\) | \(363046435271/231491250\) | \(-466684948007314571250\) | \([]\) | \(9517824\) | \(2.6550\) | \(\Gamma_0(N)\)-optimal |
| 164730.r1 | 164730cn2 | \([1, 1, 0, -21926002, -45628725476]\) | \(-578246319844489/111328125000\) | \(-224436820948423828125000\) | \([]\) | \(28553472\) | \(3.2043\) |
Rank
sage: E.rank()
The elliptic curves in class 164730cn have rank \(1\).
Complex multiplication
The elliptic curves in class 164730cn do not have complex multiplication.Modular form 164730.2.a.cn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
