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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 250173b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250173.b2 | 250173b1 | \([0, 0, 1, -6076713, 5759809240]\) | \(723570336280576/853577109\) | \(29274662291772423141\) | \([]\) | \(14976000\) | \(2.6469\) | \(\Gamma_0(N)\)-optimal |
| 250173.b1 | 250173b2 | \([0, 0, 1, -170508603, -856585839470]\) | \(15985030403346927616/8374342621029\) | \(287210199947173496599221\) | \([]\) | \(74880000\) | \(3.4517\) |
Rank
sage: E.rank()
The elliptic curves in class 250173b have rank \(2\).
Complex multiplication
The elliptic curves in class 250173b do not have complex multiplication.Modular form 250173.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
