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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 155316.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155316.d1 | 155316o4 | \([0, -1, 0, -3380588, 2393539608]\) | \(2640279346000/3087\) | \(4995596219459328\) | \([2]\) | \(2903040\) | \(2.2954\) | |
| 155316.d2 | 155316o3 | \([0, -1, 0, -209553, 38094810]\) | \(-10061824000/352947\) | \(-35697697984886448\) | \([2]\) | \(1451520\) | \(1.9488\) | |
| 155316.d3 | 155316o2 | \([0, -1, 0, -52388, 1495704]\) | \(9826000/5103\) | \(8258026403596032\) | \([2]\) | \(967680\) | \(1.7461\) | |
| 155316.d4 | 155316o1 | \([0, -1, 0, 12327, 175518]\) | \(2048000/1323\) | \(-133810613021232\) | \([2]\) | \(483840\) | \(1.3995\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155316.d have rank \(1\).
Complex multiplication
The elliptic curves in class 155316.d do not have complex multiplication.Modular form 155316.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
