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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 94192z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94192.i2 | 94192z1 | \([0, -1, 0, -81792576, -486267769088]\) | \(-1018411856981/1129900996\) | \(-67140152062983270668386304\) | \([]\) | \(17149440\) | \(3.6503\) | \(\Gamma_0(N)\)-optimal |
| 94192.i1 | 94192z2 | \([0, -1, 0, -60599681616, -5741853392379968]\) | \(-414183515883649725221/50176\) | \(-2981521639363391258624\) | \([]\) | \(85747200\) | \(4.4550\) |
Rank
sage: E.rank()
The elliptic curves in class 94192z have rank \(1\).
Complex multiplication
The elliptic curves in class 94192z do not have complex multiplication.Modular form 94192.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
