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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 30960.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.bl1 | 30960x2 | \([0, 0, 0, -46467, 3854466]\) | \(137627865747/36980\) | \(2981385584640\) | \([2]\) | \(73728\) | \(1.3771\) | |
30960.bl2 | 30960x1 | \([0, 0, 0, -3267, 44226]\) | \(47832147/17200\) | \(1386690969600\) | \([2]\) | \(36864\) | \(1.0306\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.bl do not have complex multiplication.Modular form 30960.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.