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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 94192.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94192.v1 | 94192w2 | \([0, 1, 0, -72056696, -235452843052]\) | \(-414183515883649725221/50176\) | \(-5012449132544\) | \([]\) | \(2956800\) | \(2.7714\) | |
| 94192.v2 | 94192w1 | \([0, 1, 0, -97256, -19971532]\) | \(-1018411856981/1129900996\) | \(-112874108483354624\) | \([]\) | \(591360\) | \(1.9667\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94192.v have rank \(1\).
Complex multiplication
The elliptic curves in class 94192.v do not have complex multiplication.Modular form 94192.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
