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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 50400bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.f3 | 50400bb1 | \([0, 0, 0, -973425, -300827000]\) | \(139927692143296/27348890625\) | \(19937341265625000000\) | \([2, 2]\) | \(884736\) | \(2.4200\) | \(\Gamma_0(N)\)-optimal |
| 50400.f4 | 50400bb2 | \([0, 0, 0, 2003325, -1780271750]\) | \(152461584507448/322998046875\) | \(-1883724609375000000000\) | \([2]\) | \(1769472\) | \(2.7666\) | |
| 50400.f2 | 50400bb3 | \([0, 0, 0, -4770300, 3739048000]\) | \(257307998572864/19456203375\) | \(907748624664000000000\) | \([2]\) | \(1769472\) | \(2.7666\) | |
| 50400.f1 | 50400bb4 | \([0, 0, 0, -14754675, -21813358250]\) | \(60910917333827912/3255076125\) | \(18983603961000000000\) | \([2]\) | \(1769472\) | \(2.7666\) |
Rank
sage: E.rank()
The elliptic curves in class 50400bb have rank \(0\).
Complex multiplication
The elliptic curves in class 50400bb do not have complex multiplication.Modular form 50400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
