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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 104742g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104742.r2 | 104742g1 | \([1, -1, 0, 199863, -20520563]\) | \(8181353375/6412032\) | \(-691974715056590592\) | \([2]\) | \(1622016\) | \(2.1112\) | \(\Gamma_0(N)\)-optimal |
| 104742.r1 | 104742g2 | \([1, -1, 0, -942777, -176605187]\) | \(858729462625/371764272\) | \(40120117333385242032\) | \([2]\) | \(3244032\) | \(2.4578\) |
Rank
sage: E.rank()
The elliptic curves in class 104742g have rank \(1\).
Complex multiplication
The elliptic curves in class 104742g do not have complex multiplication.Modular form 104742.2.a.g
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.
