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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1014.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1014.d1 | 1014e4 | \([1, 1, 1, -3504979, 2524207265]\) | \(986551739719628473/111045168\) | \(535993816308912\) | \([2]\) | \(26880\) | \(2.2506\) | |
| 1014.d2 | 1014e3 | \([1, 1, 1, -395379, -32619423]\) | \(1416134368422073/725251155408\) | \(3500648804183733072\) | \([2]\) | \(26880\) | \(2.2506\) | |
| 1014.d3 | 1014e2 | \([1, 1, 1, -219619, 39160961]\) | \(242702053576633/2554695936\) | \(12331029336148224\) | \([2, 2]\) | \(13440\) | \(1.9040\) | |
| 1014.d4 | 1014e1 | \([1, 1, 1, -3299, 1521281]\) | \(-822656953/207028224\) | \(-999285694857216\) | \([4]\) | \(6720\) | \(1.5574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1014.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1014.d do not have complex multiplication.Modular form 1014.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
