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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 64400.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.bb1 | 64400bi1 | \([0, 0, 0, -65075, 6387250]\) | \(476196576129/197225\) | \(12622400000000\) | \([2]\) | \(221184\) | \(1.4758\) | \(\Gamma_0(N)\)-optimal |
64400.bb2 | 64400bi2 | \([0, 0, 0, -55075, 8417250]\) | \(-288673724529/311181605\) | \(-19915622720000000\) | \([2]\) | \(442368\) | \(1.8224\) |
Rank
sage: E.rank()
The elliptic curves in class 64400.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.bb do not have complex multiplication.Modular form 64400.2.a.bb
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.