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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 79200df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79200.bw2 | 79200df1 | \([0, 0, 0, -938325, 349846000]\) | \(125330290485184/378125\) | \(275653125000000\) | \([2]\) | \(552960\) | \(1.9986\) | \(\Gamma_0(N)\)-optimal |
| 79200.bw1 | 79200df2 | \([0, 0, 0, -950700, 340144000]\) | \(2036792051776/107421875\) | \(5011875000000000000\) | \([2]\) | \(1105920\) | \(2.3451\) |
Rank
sage: E.rank()
The elliptic curves in class 79200df have rank \(1\).
Complex multiplication
The elliptic curves in class 79200df do not have complex multiplication.Modular form 79200.2.a.df
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
