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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 4800.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.bb1 | 4800e2 | \([0, -1, 0, -833, -9213]\) | \(-102400/3\) | \(-1875000000\) | \([]\) | \(2400\) | \(0.55819\) | |
4800.bb2 | 4800e1 | \([0, -1, 0, 7, 27]\) | \(20480/243\) | \(-388800\) | \([]\) | \(480\) | \(-0.24652\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.bb do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.