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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 248430.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248430.gb1 | 248430gb4 | \([1, 1, 1, -716542681, -7382930376697]\) | \(71647584155243142409/10140000\) | \(5758194215695740000\) | \([2]\) | \(61931520\) | \(3.4527\) | |
| 248430.gb2 | 248430gb3 | \([1, 1, 1, -51412761, -78990859641]\) | \(26465989780414729/10571870144160\) | \(6003439991438718044230560\) | \([2]\) | \(61931520\) | \(3.4527\) | |
| 248430.gb3 | 248430gb2 | \([1, 1, 1, -44787961, -115350411961]\) | \(17496824387403529/6580454400\) | \(3736837718217907430400\) | \([2, 2]\) | \(30965760\) | \(3.1061\) | |
| 248430.gb4 | 248430gb1 | \([1, 1, 1, -2389241, -2349343417]\) | \(-2656166199049/2658140160\) | \(-1509476064479344066560\) | \([2]\) | \(15482880\) | \(2.7595\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248430.gb have rank \(1\).
Complex multiplication
The elliptic curves in class 248430.gb do not have complex multiplication.Modular form 248430.2.a.gb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
