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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 59248.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.bb1 | 59248u2 | \([0, -1, 0, -1472912, 687684032]\) | \(582810602977/829472\) | \(502954495674810368\) | \([2]\) | \(1013760\) | \(2.2995\) | |
59248.bb2 | 59248u1 | \([0, -1, 0, -118672, 4063680]\) | \(304821217/164864\) | \(99966110941577216\) | \([2]\) | \(506880\) | \(1.9530\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59248.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 59248.bb do not have complex multiplication.Modular form 59248.2.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.