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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 30576bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30576.i4 | 30576bs1 | \([0, -1, 0, 376, -6096]\) | \(12167/39\) | \(-18793721856\) | \([2]\) | \(18432\) | \(0.65459\) | \(\Gamma_0(N)\)-optimal |
30576.i3 | 30576bs2 | \([0, -1, 0, -3544, -68816]\) | \(10218313/1521\) | \(732955152384\) | \([2, 2]\) | \(36864\) | \(1.0012\) | |
30576.i2 | 30576bs3 | \([0, -1, 0, -15304, 665008]\) | \(822656953/85683\) | \(41289806917632\) | \([2]\) | \(73728\) | \(1.3477\) | |
30576.i1 | 30576bs4 | \([0, -1, 0, -54504, -4879440]\) | \(37159393753/1053\) | \(507430490112\) | \([2]\) | \(73728\) | \(1.3477\) |
Rank
sage: E.rank()
The elliptic curves in class 30576bs have rank \(1\).
Complex multiplication
The elliptic curves in class 30576bs do not have complex multiplication.Modular form 30576.2.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.