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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3192.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3192.p1 | 3192g1 | \([0, 1, 0, -4955392, -4246324048]\) | \(13141891860831409148932/4237307541832617\) | \(4339002922836599808\) | \([2]\) | \(94080\) | \(2.5506\) | \(\Gamma_0(N)\)-optimal |
| 3192.p2 | 3192g2 | \([0, 1, 0, -4283112, -5439217680]\) | \(-4242991426585187031506/3781894171664380023\) | \(-7745319263568650287104\) | \([2]\) | \(188160\) | \(2.8972\) |
Rank
sage: E.rank()
The elliptic curves in class 3192.p have rank \(1\).
Complex multiplication
The elliptic curves in class 3192.p do not have complex multiplication.Modular form 3192.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
