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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 24336bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24336.bz4 | 24336bs1 | \([0, 0, 0, -475059, 2631149170]\) | \(-822656953/207028224\) | \(-2983851096272529260544\) | \([2]\) | \(1290240\) | \(2.7999\) | \(\Gamma_0(N)\)-optimal |
| 24336.bz3 | 24336bs2 | \([0, 0, 0, -31625139, 67828266610]\) | \(242702053576633/2554695936\) | \(36820256301269218492416\) | \([2, 2]\) | \(2580480\) | \(3.1464\) | |
| 24336.bz2 | 24336bs3 | \([0, 0, 0, -56934579, -56081689742]\) | \(1416134368422073/725251155408\) | \(10452881318911760013262848\) | \([2]\) | \(5160960\) | \(3.4930\) | |
| 24336.bz1 | 24336bs4 | \([0, 0, 0, -504716979, 4364353739122]\) | \(986551739719628473/111045168\) | \(1600468959597350289408\) | \([2]\) | \(5160960\) | \(3.4930\) |
Rank
sage: E.rank()
The elliptic curves in class 24336bs have rank \(1\).
Complex multiplication
The elliptic curves in class 24336bs do not have complex multiplication.Modular form 24336.2.a.bs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
