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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 43320bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43320.bd4 | 43320bg1 | \([0, 1, 0, 7100, -399520]\) | \(3286064/7695\) | \(-92676621899520\) | \([4]\) | \(138240\) | \(1.3640\) | \(\Gamma_0(N)\)-optimal |
| 43320.bd3 | 43320bg2 | \([0, 1, 0, -57880, -4454272]\) | \(445138564/81225\) | \(3913012924646400\) | \([2, 2]\) | \(276480\) | \(1.7106\) | |
| 43320.bd2 | 43320bg3 | \([0, 1, 0, -274480, 51168608]\) | \(23735908082/1954815\) | \(188346355439646720\) | \([2]\) | \(552960\) | \(2.0572\) | |
| 43320.bd1 | 43320bg4 | \([0, 1, 0, -880960, -318541600]\) | \(784767874322/35625\) | \(3432467477760000\) | \([2]\) | \(552960\) | \(2.0572\) |
Rank
sage: E.rank()
The elliptic curves in class 43320bg have rank \(1\).
Complex multiplication
The elliptic curves in class 43320bg do not have complex multiplication.Modular form 43320.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
