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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 29400dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.dl3 | 29400dz1 | \([0, 1, 0, -8983, 322538]\) | \(2725888/21\) | \(617657250000\) | \([2]\) | \(49152\) | \(1.0915\) | \(\Gamma_0(N)\)-optimal |
| 29400.dl2 | 29400dz2 | \([0, 1, 0, -15108, -179712]\) | \(810448/441\) | \(207532836000000\) | \([2, 2]\) | \(98304\) | \(1.4381\) | |
| 29400.dl4 | 29400dz3 | \([0, 1, 0, 58392, -1355712]\) | \(11696828/7203\) | \(-13558811952000000\) | \([2]\) | \(196608\) | \(1.7846\) | |
| 29400.dl1 | 29400dz4 | \([0, 1, 0, -186608, -31049712]\) | \(381775972/567\) | \(1067311728000000\) | \([2]\) | \(196608\) | \(1.7846\) |
Rank
sage: E.rank()
The elliptic curves in class 29400dz have rank \(0\).
Complex multiplication
The elliptic curves in class 29400dz do not have complex multiplication.Modular form 29400.2.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 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.
