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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 94640.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.bz1 | 94640cj4 | \([0, 0, 0, -723827, 237016754]\) | \(2121328796049/120050\) | \(2373461690163200\) | \([2]\) | \(737280\) | \(2.0146\) | |
| 94640.bz2 | 94640cj3 | \([0, 0, 0, -237107, -41527694]\) | \(74565301329/5468750\) | \(108120521600000000\) | \([2]\) | \(737280\) | \(2.0146\) | |
| 94640.bz3 | 94640cj2 | \([0, 0, 0, -47827, 3255954]\) | \(611960049/122500\) | \(2421899683840000\) | \([2, 2]\) | \(368640\) | \(1.6680\) | |
| 94640.bz4 | 94640cj1 | \([0, 0, 0, 6253, 303186]\) | \(1367631/2800\) | \(-55357707059200\) | \([2]\) | \(184320\) | \(1.3215\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94640.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 94640.bz do not have complex multiplication.Modular form 94640.2.a.bz
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
