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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 193600.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.bb1 | 193600l2 | \([0, 1, 0, -13713, 606703]\) | \(78608\) | \(3628156928000\) | \([2]\) | \(327680\) | \(1.2189\) | |
| 193600.bb2 | 193600l1 | \([0, 1, 0, -1613, -10397]\) | \(2048\) | \(226759808000\) | \([2]\) | \(163840\) | \(0.87230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193600.bb have rank \(2\).
Complex multiplication
The elliptic curves in class 193600.bb do not have complex multiplication.Modular form 193600.2.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.
