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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 19110bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19110.bc2 | 19110bb1 | \([1, 0, 1, -2574, 52672]\) | \(-16022066761/998400\) | \(-117460761600\) | \([2]\) | \(28800\) | \(0.87822\) | \(\Gamma_0(N)\)-optimal |
19110.bc1 | 19110bb2 | \([1, 0, 1, -41774, 3282752]\) | \(68523370149961/243360\) | \(28631060640\) | \([2]\) | \(57600\) | \(1.2248\) |
Rank
sage: E.rank()
The elliptic curves in class 19110bb have rank \(0\).
Complex multiplication
The elliptic curves in class 19110bb do not have complex multiplication.Modular form 19110.2.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 Cremona 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 Cremona labels.