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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 1950bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.v2 | 1950bb1 | \([1, 0, 0, -323, -63]\) | \(29819839301/17252352\) | \(2156544000\) | \([2]\) | \(1792\) | \(0.48045\) | \(\Gamma_0(N)\)-optimal |
1950.v1 | 1950bb2 | \([1, 0, 0, -3523, 79937]\) | \(38686490446661/141927552\) | \(17740944000\) | \([2]\) | \(3584\) | \(0.82703\) |
Rank
sage: E.rank()
The elliptic curves in class 1950bb have rank \(1\).
Complex multiplication
The elliptic curves in class 1950bb do not have complex multiplication.Modular form 1950.2.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.