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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 14400.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.dz1 | 14400dw3 | \([0, 0, 0, -37200, -2761000]\) | \(488095744/125\) | \(1458000000000\) | \([2]\) | \(27648\) | \(1.3200\) | |
| 14400.dz2 | 14400dw4 | \([0, 0, 0, -32700, -3454000]\) | \(-20720464/15625\) | \(-2916000000000000\) | \([2]\) | \(55296\) | \(1.6665\) | |
| 14400.dz3 | 14400dw1 | \([0, 0, 0, -1200, 11000]\) | \(16384/5\) | \(58320000000\) | \([2]\) | \(9216\) | \(0.77065\) | \(\Gamma_0(N)\)-optimal |
| 14400.dz4 | 14400dw2 | \([0, 0, 0, 3300, 74000]\) | \(21296/25\) | \(-4665600000000\) | \([2]\) | \(18432\) | \(1.1172\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.dz do not have complex multiplication.Modular form 14400.2.a.dz
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.
